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Transportation Distance between Probability Measures on the Infinite Regular Tree SIAM J. Discret. Math. (IF 0.8) Pub Date : 2024-03-15 Pakawut Jiradilok, Supanat Kamtue
SIAM Journal on Discrete Mathematics, Volume 38, Issue 1, Page 1113-1157, March 2024. Abstract. In the infinite regular tree [math] with [math], we consider families [math], indexed by vertices [math] and nonnegative integers (“discrete time steps”) [math], of probability measures such that [math] if the distances [math] and [math] are equal. Let [math] be a positive integer, and let [math] and [math]
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Rainbow Saturation for Complete Graphs SIAM J. Discret. Math. (IF 0.8) Pub Date : 2024-03-14 Debsoumya Chakraborti, Kevin Hendrey, Ben Lund, Casey Tompkins
SIAM Journal on Discrete Mathematics, Volume 38, Issue 1, Page 1090-1112, March 2024. Abstract. We call an edge-colored graph rainbow if all of its edges receive distinct colors. An edge-colored graph [math] is called [math]-rainbow saturated if [math] does not contain a rainbow copy of [math] and adding an edge of any color to [math] creates a rainbow copy of [math]. The rainbow saturation number
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Shallow Minors, Graph Products, and Beyond-Planar Graphs SIAM J. Discret. Math. (IF 0.8) Pub Date : 2024-03-13 Robert Hickingbotham, David R. Wood
SIAM Journal on Discrete Mathematics, Volume 38, Issue 1, Page 1057-1089, March 2024. Abstract. The planar graph product structure theorem of Dujmović et al. [J. ACM, 67 (2020), 22] states that every planar graph is a subgraph of the strong product of a graph with bounded treewidth and a path. This result has been the key tool to resolve important open problems regarding queue layouts, nonrepetitive
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Online Spanners in Metric Spaces SIAM J. Discret. Math. (IF 0.8) Pub Date : 2024-03-12 Sujoy Bhore, Arnold Filtser, Hadi Khodabandeh, Csaba D. Tóth
SIAM Journal on Discrete Mathematics, Volume 38, Issue 1, Page 1030-1056, March 2024. Abstract. Given a metric space [math], a weighted graph [math] over [math] is a metric [math]-spanner of [math] if for every [math], [math], where [math] is the shortest path metric in [math]. In this paper, we construct spanners for finite sets in metric spaces in the online setting. Here, we are given a sequence
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Don’t Roll the Dice, Ask Twice: The Two-Query Distortion of Matching Problems and Beyond SIAM J. Discret. Math. (IF 0.8) Pub Date : 2024-03-12 Georgios Amanatidis, Georgios Birmpas, Aris Filos-Ratsikas, Alexandros A. Voudouris
SIAM Journal on Discrete Mathematics, Volume 38, Issue 1, Page 1007-1029, March 2024. Abstract. In most social choice settings, the participating agents express their preferences over the different alternatives in the form of linear orderings. While this clearly simplifies preference elicitation, it inevitably leads to poor performance with respect to optimizing a cardinal objective, such as the social
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On the Concentration of the Maximum Degree in the Duplication-Divergence Models SIAM J. Discret. Math. (IF 0.8) Pub Date : 2024-03-07 Alan M. Frieze, Krzysztof Turowski, Wojciech Szpankowski
SIAM Journal on Discrete Mathematics, Volume 38, Issue 1, Page 988-1006, March 2024. Abstract. We present a rigorous and precise analysis of the maximum degree and the average degree in a dynamic duplication-divergence graph model introduced by Solé et al. [Adv. Complex Syst., 5 (2002), pp. 43–54] in which the graph grows according to a duplication-divergence mechanism, i.e., by iteratively creating
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Treewidth, Circle Graphs, and Circular Drawings SIAM J. Discret. Math. (IF 0.8) Pub Date : 2024-03-06 Robert Hickingbotham, Freddie Illingworth, Bojan Mohar, David R. Wood
SIAM Journal on Discrete Mathematics, Volume 38, Issue 1, Page 965-987, March 2024. Abstract. A circle graph is an intersection graph of a set of chords of a circle. We describe the unavoidable induced subgraphs of circle graphs with large treewidth. This includes examples that are far from the “usual suspects.” Our results imply that treewidth and Hadwiger number are linearly tied on the class of
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Eigenpolytope Universality and Graphical Designs SIAM J. Discret. Math. (IF 0.8) Pub Date : 2024-03-05 Catherine Babecki, David Shiroma
SIAM Journal on Discrete Mathematics, Volume 38, Issue 1, Page 947-964, March 2024. Abstract. We show that the eigenpolytopes of graphs are universal in the sense that every polytope, up to affine equivalence, appears as the eigenpolytope of some positively weighted graph. We next extend the theory of graphical designs, which are quadrature rules for graphs, to positively weighted graphs. Through Gale
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On [math]-Counting of Noncrossing Chains and Parking Functions SIAM J. Discret. Math. (IF 0.8) Pub Date : 2024-03-05 Yen-Jen Cheng, Sen-Peng Eu, Tung-Shan Fu, Jyun-Cheng Yao
SIAM Journal on Discrete Mathematics, Volume 38, Issue 1, Page 917-946, March 2024. Abstract. For a finite Coxeter group [math], Josuat-Vergès derived a [math]-polynomial counting the maximal chains in the lattice of noncrossing partitions of [math] by weighting some of the covering relations, which we call bad edges, in these chains with a parameter [math]. We study the connection of these weighted
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Robust Factorizations and Colorings of Tensor Graphs SIAM J. Discret. Math. (IF 0.8) Pub Date : 2024-02-28 Joshua Brakensiek, Sami Davies
SIAM Journal on Discrete Mathematics, Volume 38, Issue 1, Page 883-916, March 2024. Abstract. Since the seminal result of Karger, Motwani, and Sudan, algorithms for approximate 3-coloring have primarily centered around rounding the solution to a Semidefinite Program. However, it is likely that important combinatorial or algebraic insights are needed in order to break the [math] threshold. One way to
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Rainbow Spanning Trees in Randomly Colored [math] SIAM J. Discret. Math. (IF 0.8) Pub Date : 2024-02-27 Deepak Bal, Alan Frieze, Paweł Prałat
SIAM Journal on Discrete Mathematics, Volume 38, Issue 1, Page 867-882, March 2024. Abstract. Given a graph [math] on [math] vertices and an assignment of colors to its edges, a set of edges [math] is said to be rainbow if edges from [math] have pairwise different colors assigned to them. In this paper, we investigate rainbow spanning trees in randomly colored random [math] graphs.
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Cops and Robbers on [math]-Free Graphs SIAM J. Discret. Math. (IF 0.8) Pub Date : 2024-02-26 Maria Chudnovsky, Sergey Norin, Paul D. Seymour, Jérémie Turcotte
SIAM Journal on Discrete Mathematics, Volume 38, Issue 1, Page 845-856, March 2024. Abstract. We prove that every connected [math]-free graph has cop number at most two, solving a conjecture of Sivaraman. In order to do so, we first prove that every connected [math]-free graph [math] with independence number at least three contains a three-vertex induced path with vertices [math] in order, such that
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Pathwidth Versus Cocircumference SIAM J. Discret. Math. (IF 0.8) Pub Date : 2024-02-26 Marcin Briański, Gwenaël Joret, Michał T. Seweryn
SIAM Journal on Discrete Mathematics, Volume 38, Issue 1, Page 857-866, March 2024. Abstract. The circumference of a graph [math] with at least one cycle is the length of a longest cycle in [math]. A classic result of Birmelé [J. Graph Theory, 43 (2003), pp. 24–25] states that the treewidth of [math] is at most its circumference minus 1. In case [math] is 2-connected, this upper bound also holds for
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Strong Cocomparability Graphs and Slash-Free Orderings of Matrices SIAM J. Discret. Math. (IF 0.8) Pub Date : 2024-02-12 Pavol Hell, Jing Huang, Jephian C.-H. Lin
SIAM Journal on Discrete Mathematics, Volume 38, Issue 1, Page 828-844, March 2024. Abstract. We introduce the class of strong cocomparability graphs, as the class of reflexive graphs whose adjacency matrix can be rearranged by a simultaneous row and column permutation to avoid the submatrix with rows 01,10, which we call Slash. We provide an ordering characterization, a forbidden structure characterization
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Stable Approximation Algorithms for the Dynamic Broadcast Range-Assignment Problem SIAM J. Discret. Math. (IF 0.8) Pub Date : 2024-02-09 Mark de Berg, Arpan Sadhukhan, Frits Spieksma
SIAM Journal on Discrete Mathematics, Volume 38, Issue 1, Page 790-827, March 2024. Abstract. Let [math] be a set of points in [math], where each point [math] has an associated transmission range, denoted [math]. The range assignment [math] induces a directed communication graph [math] on [math], which contains an edge [math] iff [math]. In the broadcast range-assignment problem, the goal is to assign
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Fractionally Subadditive Maximization under an Incremental Knapsack Constraint with Applications to Incremental Flows SIAM J. Discret. Math. (IF 0.8) Pub Date : 2024-02-06 Yann Disser, Max Klimm, Annette Lutz, David Weckbecker
SIAM Journal on Discrete Mathematics, Volume 38, Issue 1, Page 764-789, March 2024. Abstract. We consider the problem of maximizing a fractionally subadditive function under an increasing knapsack constraint. An incremental solution to this problem is given by an order in which to include the elements of the ground set, and the competitive ratio of an incremental solution is defined by the worst ratio
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Global Rigidity of Line Constrained Frameworks SIAM J. Discret. Math. (IF 0.8) Pub Date : 2024-02-06 James Cruickshank, Fatemeh Mohammadi, Harshit J. Motwani, Anthony Nixon, Shin-ichi Tanigawa
SIAM Journal on Discrete Mathematics, Volume 38, Issue 1, Page 743-763, March 2024. Abstract. We consider the global rigidity problem for bar-joint frameworks where each vertex is constrained to lie on a particular line in [math]. In our setting, we allow multiple vertices to be constrained to the same line. We give a combinatorial characterization of generic rigidity in this setting for arbitrary
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Bernoulli Factories for Flow-Based Polytopes SIAM J. Discret. Math. (IF 0.8) Pub Date : 2024-02-06 Rad Niazadeh, Renato Paes Leme, Jon Schneider
SIAM Journal on Discrete Mathematics, Volume 38, Issue 1, Page 726-742, March 2024. Abstract. We construct explicit combinatorial Bernoulli factories for the following class of flow-based polytopes: integral 0/1-polytopes defined by a set of network flow constraints. This generalizes the results of Niazadeh et al. (who constructed an explicit factory for the specific case of bipartite perfect matchings)
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Rapid Mixing of [math]-Class Biased Permutations SIAM J. Discret. Math. (IF 0.8) Pub Date : 2024-02-06 Sarah Miracle, Amanda Pascoe Streib
SIAM Journal on Discrete Mathematics, Volume 38, Issue 1, Page 702-725, March 2024. Abstract. In this paper, we study a biased version of the nearest-neighbor transposition Markov chain on the set of permutations where neighboring elements [math] and [math] are placed in order [math] with probability [math]. Our goal is to identify the class of parameter sets [math] for which this Markov chain is rapidly
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Some Cubic Time Regularity Algorithms for Triple Systems SIAM J. Discret. Math. (IF 0.8) Pub Date : 2024-02-05 Brendan Nagle, John Theado
SIAM Journal on Discrete Mathematics, Volume 38, Issue 1, Page 668-701, March 2024. Abstract. Szemerédi’s regularity lemma guarantees that, for fixed [math], every graph [math] admits an [math]-regular and [math]-equitable partition [math], where [math]. These partitions are constructed by Kohayakawa, Rödl, and Thoma in time [math]. Analogous partitions of [math]-graphs [math] are constructed by Czygrinow
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Pure Pairs. IX. Transversal Trees SIAM J. Discret. Math. (IF 0.8) Pub Date : 2024-02-02 Alex Scott, Paul Seymour, Sophie T. Spirkl
SIAM Journal on Discrete Mathematics, Volume 38, Issue 1, Page 645-667, March 2024. Abstract. Fix [math], and let [math] be a graph, with vertex set partitioned into [math] subsets (“blocks”) of approximately equal size. An induced subgraph of [math] is “transversal” (with respect to this partition) if it has exactly one vertex in each block (and therefore it has exactly [math] vertices). A “pure pair”
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Graphs without a Rainbow Path of Length 3 SIAM J. Discret. Math. (IF 0.8) Pub Date : 2024-02-02 Sebastian Babiński, Andrzej Grzesik
SIAM Journal on Discrete Mathematics, Volume 38, Issue 1, Page 629-644, March 2024. Abstract. In 1959, Erdős and Gallai proved the asymptotically optimal bound for the maximum number of edges in graphs not containing a path of a fixed length. Here, we study a rainbow version of their theorem, in which one considers [math] graphs on a common set of vertices not creating a path having edges from different
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Canonical Theorems for Colored Integers with Respect to Some Linear Combinations SIAM J. Discret. Math. (IF 0.8) Pub Date : 2024-02-01 Maria Axenovich, Hanno Lefmann
SIAM Journal on Discrete Mathematics, Volume 38, Issue 1, Page 609-628, March 2024. Abstract. Hindman proved in 1979 that no matter how natural numbers are colored in [math] colors, for a fixed positive integer [math], there is an infinite subset [math] of numbers and a color [math] such that for any finite nonempty subset [math] of [math], the color of the sum of elements from [math] is [math]. Later
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Graph Limits and Spectral Extremal Problems for Graphs SIAM J. Discret. Math. (IF 0.8) Pub Date : 2024-01-31 Lele Liu
SIAM Journal on Discrete Mathematics, Volume 38, Issue 1, Page 590-608, March 2024. Abstract. We prove two conjectures in spectral extremal graph theory involving the linear combinations of graph eigenvalues. Let [math] be the largest eigenvalue of the adjacency matrix of a graph [math] and [math] be the complement of [math]. A nice conjecture states that the graph on [math] vertices maximizing [math]
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[math]-Modules in Graphs SIAM J. Discret. Math. (IF 0.8) Pub Date : 2024-01-29 Michel Habib, Lalla Mouatadid, Éric Sopena, Mengchuan Zou
SIAM Journal on Discrete Mathematics, Volume 38, Issue 1, Page 566-589, March 2024. Abstract. Modular decomposition focuses on repeatedly identifying a module [math] (a collection of vertices that shares exactly the same neighborhood outside of [math]) and collapsing it into a single vertex. This notion of exactitude of neighborhood is very strict, especially when dealing with real-world graphs. We
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The Power of Filling in Balanced Allocations SIAM J. Discret. Math. (IF 0.8) Pub Date : 2024-01-29 Dimitrios Los, Thomas Sauerwald, John Sylvester
SIAM Journal on Discrete Mathematics, Volume 38, Issue 1, Page 529-565, March 2024. Abstract. We introduce a new class of balanced allocation processes which are primarily characterized by “filling” underloaded bins. A prototypical example is the Packing process: At each round we only take one bin sample, and if the load is below the average load, then we place as many balls until the average load
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On the Combinatorial Diameters of Parallel and Series Connections SIAM J. Discret. Math. (IF 0.8) Pub Date : 2024-01-22 Steffen Borgwardt, Weston Grewe, Jon Lee
SIAM Journal on Discrete Mathematics, Volume 38, Issue 1, Page 485-503, March 2024. Abstract. The investigation of combinatorial diameters of polyhedra is a classical topic in linear programming due to its connection with the possibility of an efficient pivot rule for the simplex method. We are interested in the diameters of polyhedra formed from the so-called parallel or series connection of oriented
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Isomorphism Testing Parameterized by Genus and Beyond SIAM J. Discret. Math. (IF 0.8) Pub Date : 2024-01-22 Daniel Neuen
SIAM Journal on Discrete Mathematics, Volume 38, Issue 1, Page 453-484, March 2024. Abstract. We present an isomorphism test for graphs of Euler genus [math] running in time [math]. Our algorithm provides the first explicit upper bound on the dependence on [math] for an fpt isomorphism test parameterized by the Euler genus of the input graphs. The only previous fpt algorithm runs in time [math] for
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Optimal Sets of Questions for Twenty Questions SIAM J. Discret. Math. (IF 0.8) Pub Date : 2024-01-19 Yuval Filmus, Idan Mehalel
SIAM Journal on Discrete Mathematics, Volume 38, Issue 1, Page 412-452, March 2024. Abstract. In the distributional Twenty Questions game, Bob chooses a number [math] from 1 to [math] according to a distribution [math], and Alice (who knows [math]) attempts to identify [math] using yes/no questions, which Bob answers truthfully. Her goal is to minimize the expected number of questions. The optimal
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Convex Characters, Algorithms, and Matchings SIAM J. Discret. Math. (IF 0.8) Pub Date : 2024-01-19 Steven Kelk, Ruben Meuwese, Stephan Wagner
SIAM Journal on Discrete Mathematics, Volume 38, Issue 1, Page 380-411, March 2024. Abstract. Phylogenetic trees are used to model evolution: leaves are labeled to represent contemporary species (“taxa”), and interior vertices represent extinct ancestors. Informally, convex characters are measurements on the contemporary species in which the subset of species (both contemporary and extinct) that share
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Square Coloring Planar Graphs with Automatic Discharging SIAM J. Discret. Math. (IF 0.8) Pub Date : 2024-01-23 Nicolas Bousquet, Quentin Deschamps, Lucas De Meyer, Théo Pierron
SIAM Journal on Discrete Mathematics, Volume 38, Issue 1, Page 504-528, March 2024. Abstract. The discharging method is a powerful proof technique, especially for graph coloring problems. Its major downside is that it often requires lengthy case analyses, which are sometimes given to a computer for verification. However, it is much less common to use a computer to actively look for a discharging proof
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Unified Greedy Approximability beyond Submodular Maximization SIAM J. Discret. Math. (IF 0.8) Pub Date : 2024-01-18 Yann Disser, David Weckbecker
SIAM Journal on Discrete Mathematics, Volume 38, Issue 1, Page 348-379, March 2024. Abstract. We consider classes of objective functions of cardinality-constrained maximization problems for which the greedy algorithm guarantees a constant approximation. We propose the new class of [math]-[math]-augmentable functions and prove that it encompasses several important subclasses, such as functions of bounded
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Invertibility of Digraphs and Tournaments SIAM J. Discret. Math. (IF 0.8) Pub Date : 2024-01-16 Noga Alon, Emil Powierski, Michael Savery, Alex Scott, Elizabeth Wilmer
SIAM Journal on Discrete Mathematics, Volume 38, Issue 1, Page 327-347, March 2024. Abstract. For an oriented graph [math] and a set [math], the inversion of [math] in [math] is the digraph obtained by reversing the orientations of the edges of [math] with both endpoints in [math]. The inversion number of [math], [math], is the minimum number of inversions which can be applied in turn to [math] to
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A Property on Monochromatic Copies of Graphs Containing a Triangle SIAM J. Discret. Math. (IF 0.8) Pub Date : 2024-01-12 Hao Chen, Jie Ma
SIAM Journal on Discrete Mathematics, Volume 38, Issue 1, Page 316-326, March 2024. Abstract. A graph [math] is called common and, respectively, strongly common if the number of monochromatic copies of [math] in a 2-edge-coloring [math] of a large clique is asymptotically minimized by the random coloring with an equal proportion of each color and, respectively, by the random coloring with the same
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Geometric Network Creation Games SIAM J. Discret. Math. (IF 0.8) Pub Date : 2024-01-11 Davide Bilò, Tobias Friedrich, Pascal Lenzner, Anna Melnichenko
SIAM Journal on Discrete Mathematics, Volume 38, Issue 1, Page 277-315, March 2024. Abstract. Network creation games are a well-known approach for explaining and analyzing the structure, quality, and dynamics of real-world networks that evolved via the interaction of selfish agents without a central authority. In these games selfish agents corresponding to nodes in a network strategically buy incident
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The Treewidth and Pathwidth of Graph Unions SIAM J. Discret. Math. (IF 0.8) Pub Date : 2024-01-10 Bogdan Alecu, Vadim V. Lozin, Daniel A. Quiroz, Roman Rabinovich, Igor Razgon, Viktor Zamaraev
SIAM Journal on Discrete Mathematics, Volume 38, Issue 1, Page 261-276, March 2024. Abstract. Given two [math]-vertex graphs [math] and [math] of bounded treewidth, is there an [math]-vertex graph [math] of bounded treewidth having subgraphs isomorphic to [math] and [math]? Our main result is a negative answer to this question, in a strong sense: we show that the answer is no even if [math] is a binary
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Highly Connected Subgraphs with Large Chromatic Number SIAM J. Discret. Math. (IF 0.8) Pub Date : 2024-01-09 Tung H. Nguyen
SIAM Journal on Discrete Mathematics, Volume 38, Issue 1, Page 243-260, March 2024. Abstract. For integers [math] and [math], let [math] be the least integer [math] such that every graph with chromatic number at least [math] contains a [math]-connected subgraph with chromatic number at least [math]. Refining the recent result of Girão and Narayanan [Bull. Lond. Math. Soc., 54 (2022), pp. 868–875] that
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On Ramsey Size-Linear Graphs and Related Questions SIAM J. Discret. Math. (IF 0.8) Pub Date : 2024-01-09 Domagoj Bradač, Lior Gishboliner, Benny Sudakov
SIAM Journal on Discrete Mathematics, Volume 38, Issue 1, Page 225-242, March 2024. Abstract. In this paper we prove several results on Ramsey numbers [math] for a fixed graph [math] and a large graph [math], in particular for [math]. These results extend earlier work of Erdős, Faudree, Rousseau, and Schelp and of Balister, Schelp, and Simonovits on so-called Ramsey size-linear graphs. Among other
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Modules in Robinson Spaces SIAM J. Discret. Math. (IF 0.8) Pub Date : 2024-01-08 Mikhael Carmona, Victor Chepoi, Guyslain Naves, Pascal Préa
SIAM Journal on Discrete Mathematics, Volume 38, Issue 1, Page 190-224, March 2024. Abstract. A Robinson space is a dissimilarity space [math] (i.e., a set [math] of size [math] and a dissimilarity [math] on [math]) for which there exists a total order [math] on [math] such that [math] implies that [math]. Recognizing if a dissimilarity space is Robinson has numerous applications in seriation and classification
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On Weighted Graph Separation Problems and Flow Augmentation SIAM J. Discret. Math. (IF 0.8) Pub Date : 2024-01-08 Eun Jung Kim, Tomáš Masařík, Marcin Pilipczuk, Roohani Sharma, Magnus Wahlström
SIAM Journal on Discrete Mathematics, Volume 38, Issue 1, Page 170-189, March 2024. Abstract. One of the first applications of the recently introduced technique of flow augmentation [Kim et al., STOC 2022] is a fixed-parameter algorithm for the weighted version of Directed Feedback Vertex Set, a landmark problem in parameterized complexity. In this article, we explore the applicability of flow augmentation
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Stochastic Probing with Increasing Precision SIAM J. Discret. Math. (IF 0.8) Pub Date : 2024-01-08 Martin Hoefer, Kevin Schewior, Daniel Schmand
SIAM Journal on Discrete Mathematics, Volume 38, Issue 1, Page 148-169, March 2024. Abstract. We consider a selection problem with stochastic probing. There is a set of items whose values are drawn from independent distributions. The distributions are known in advance. Each item can be tested repeatedly. Each test reduces the uncertainty about the realization of its value. We study a testing model
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Exchange Distance of Basis Pairs in Split Matroids SIAM J. Discret. Math. (IF 0.8) Pub Date : 2024-01-08 Kristóf Bérczi, Tamás Schwarcz
SIAM Journal on Discrete Mathematics, Volume 38, Issue 1, Page 132-147, March 2024. Abstract. The basis exchange axiom has been a driving force in the development of matroid theory. However, the axiom gives only a local characterization of the relation of bases, which is a major stumbling block to further progress, and providing a global understanding of the structure of matroid bases is a fundamental
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The Spectrum of the Grigoriev–Laurent Pseudomoments SIAM J. Discret. Math. (IF 0.8) Pub Date : 2024-01-05 Dmitriy Kunisky, Cristopher Moore
SIAM Journal on Discrete Mathematics, Volume 38, Issue 1, Page 103-131, March 2024. Abstract. Grigoriev (2001) and Laurent (2003) independently showed that the sum-of-squares hierarchy of semidefinite programs does not exactly represent the hypercube [math] until degree at least [math] of the hierarchy. Laurent also observed that the pseudomoment matrices her proof constructs appear to have surprisingly
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On a Conjecture of Feige for Discrete Log-Concave Distributions SIAM J. Discret. Math. (IF 0.8) Pub Date : 2024-01-05 Abdulmajeed Alqasem, Heshan Aravinda, Arnaud Marsiglietti, James Melbourne
SIAM Journal on Discrete Mathematics, Volume 38, Issue 1, Page 93-102, March 2024. Abstract. A remarkable conjecture of Feige [SIAM J. Comput., 35 (2006), pp. 964–984] asserts that for any collection of [math] independent nonnegative random variables [math], each with expectation at most 1, [math], where [math]. In this paper, we investigate this conjecture for the class of discrete log-concave probability
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Tangles and Hierarchical Clustering SIAM J. Discret. Math. (IF 0.8) Pub Date : 2024-01-05 Eva Fluck
SIAM Journal on Discrete Mathematics, Volume 38, Issue 1, Page 75-92, March 2024. Abstract. We establish a connection between tangles, a concept from structural graph theory that plays a central role in Robertson and Seymour’s graph minor project, and hierarchical clustering. Tangles cannot only be defined for graphs, but in fact for arbitrary connectivity functions, which are functions defined on
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Ramsey Equivalence for Asymmetric Pairs of Graphs SIAM J. Discret. Math. (IF 0.8) Pub Date : 2024-01-04 Simona Boyadzhiyska, Dennis Clemens, Pranshu Gupta, Jonathan Rollin
SIAM Journal on Discrete Mathematics, Volume 38, Issue 1, Page 55-74, March 2024. Abstract. A graph [math] is Ramsey for a pair of graphs [math] if any red/blue-coloring of the edges of [math] yields a copy of [math] with all edges colored red or a copy of [math] with all edges colored blue. Two pairs of graphs are called Ramsey equivalent if they have the same collection of Ramsey graphs. The symmetric
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Packing and Covering a Given Directed Graph in a Directed Graph SIAM J. Discret. Math. (IF 0.8) Pub Date : 2024-01-04 Raphael Yuster
SIAM Journal on Discrete Mathematics, Volume 38, Issue 1, Page 43-54, March 2024. Abstract. For every fixed [math], it is proved that if an [math]-vertex directed graph has at most [math] pairwise arc-disjoint directed [math]-cycles, then there exists a set of at most [math] arcs that meets all directed [math]-cycles and that the set of [math]-cycles admits a fractional cover of value at most [math]
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On the Erdős–Pósa Property for Long Holes in [math]-Free Graphs SIAM J. Discret. Math. (IF 0.8) Pub Date : 2024-01-03 Tony Huynh, O-joung Kwon
SIAM Journal on Discrete Mathematics, Volume 38, Issue 1, Page 19-42, March 2024. Abstract. We prove that there exists a function [math] such that for every [math]-free graph [math] and every [math], [math] contains either [math] vertex-disjoint holes of length at least 6 or a set [math] of at most [math] vertices such that [math] has no hole of length at least 6. This answers a question of Kim and
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On the Column Number and Forbidden Submatrices for [math]-Modular Matrices SIAM J. Discret. Math. (IF 0.8) Pub Date : 2024-01-03 Joseph Paat, Ingo Stallknecht, Zach Walsh, Luze Xu
SIAM Journal on Discrete Mathematics, Volume 38, Issue 1, Page 1-18, March 2024. Abstract. An integer matrix [math] is [math]-modular if the determinant of each [math] submatrix of [math] has absolute value at most [math]. The study of [math]-modular matrices appears in the theory of integer programming, where an open conjecture is whether integer programs defined by [math]-modular constraint matrices
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The Success Probability in Levine’s Hat Problem, and Independent Sets in Graphs SIAM J. Discret. Math. (IF 0.8) Pub Date : 2023-11-20 Noga Alon, Ehud Friedgut, Gil Kalai, Guy Kindler
SIAM Journal on Discrete Mathematics, Volume 37, Issue 4, Page 2717-2729, December 2023. Abstract. Lionel Levine’s hat challenge has [math] players, each with a (very large or infinite) stack of hats on their head, each hat independently colored at random black or white. The players are allowed to coordinate before the random colors are chosen, but not after. Each player sees all hats except for those
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Quasirandom-Forcing Orientations of Cycles SIAM J. Discret. Math. (IF 0.8) Pub Date : 2023-11-14 Andrzej Grzesik, Daniel Il’kovič, Bartłomiej Kielak, Daniel Král’
SIAM Journal on Discrete Mathematics, Volume 37, Issue 4, Page 2689-2716, December 2023. Abstract. An oriented graph [math] is quasirandom-forcing if the limit (homomorphism) density of [math] in a sequence of tournaments is [math] if and only if the sequence is quasirandom. We study generalizations of the following result: the cyclic orientation of a cycle of length [math] is quasirandom-forcing if
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Improved NP-Hardness of Approximation for Orthogonality Dimension and Minrank SIAM J. Discret. Math. (IF 0.8) Pub Date : 2023-11-14 Dror Chawin, Ishay Haviv
SIAM Journal on Discrete Mathematics, Volume 37, Issue 4, Page 2670-2688, December 2023. Abstract. The orthogonality dimension of a graph [math] over [math] is the smallest integer [math] for which one can assign a nonzero [math]-dimensional real vector to each vertex of [math] such that every two adjacent vertices receive orthogonal vectors. We prove that for every sufficiently large integer [math]
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Further Exploiting c-Closure for FPT Algorithms and Kernels for Domination Problems SIAM J. Discret. Math. (IF 0.8) Pub Date : 2023-11-10 Lawqueen Kanesh, Jayakrishnan Madathil, Sanjukta Roy, Abhishek Sahu, Saket Saurabh
SIAM Journal on Discrete Mathematics, Volume 37, Issue 4, Page 2626-2669, December 2023. Abstract. For a positive integer [math], a graph [math] is said to be [math]-closed if every pair of nonadjacent vertices in [math] have at most [math] neighbors in common. The closure of a graph [math], denoted by [math], is the least positive integer [math] for which [math] is [math]-closed. The class of [math]-closed
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Symmetric Layer-Rainbow Colorations of Cubes SIAM J. Discret. Math. (IF 0.8) Pub Date : 2023-11-10 Amin Bahmanian
SIAM Journal on Discrete Mathematics, Volume 37, Issue 4, Page 2617-2625, December 2023. Abstract. Can we color the [math] cells of an [math] cube [math] with [math] colors in such a way that each layer parallel to each face contains each color exactly once and that the coloring is symmetric so that [math] for distinct [math], and [math] for [math]? Using transportation networks, we show that such
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Sample Compression Schemes for Balls in Graphs SIAM J. Discret. Math. (IF 0.8) Pub Date : 2023-11-09 Jérémie Chalopin, Victor Chepoi, Fionn Mc Inerney, Sébastien Ratel, Yann Vaxès
SIAM Journal on Discrete Mathematics, Volume 37, Issue 4, Page 2585-2616, December 2023. Abstract. One of the open problems in machine learning is whether any set-family of VC-dimension [math] admits a sample compression scheme of size [math]. In this paper, we study this problem for balls in graphs. For a ball [math] of a graph [math], a realizable sample for [math] is a signed subset [math] of [math]
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A Framework for Minimal Hereditary Classes of Graphs of Unbounded Clique-Width SIAM J. Discret. Math. (IF 0.8) Pub Date : 2023-10-30 R. Brignall, D. Cocks
SIAM Journal on Discrete Mathematics, Volume 37, Issue 4, Page 2558-2584, December 2023. Abstract. We create a framework for hereditary graph classes [math] built on a two-dimensional grid of vertices and edge sets defined by a triple [math] of objects that define edges between consecutive columns, edges between nonconsecutive columns (called bonds), and edges within columns. This framework captures
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Partial Shuffles by Lazy Swaps SIAM J. Discret. Math. (IF 0.8) Pub Date : 2023-10-30 Barnabás Janzer, J. Robert Johnson, Imre Leader
SIAM Journal on Discrete Mathematics, Volume 37, Issue 4, Page 2544-2557, December 2023. Abstract. How many random transpositions (meaning that we swap given pairs of elements with given probabilities independently) are needed to ensure that each element of [math] is uniformly distributed—in the sense that the probability that [math] is mapped to [math] is [math] for all [math] and [math]? And what
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The Extremality of 2-Partite Turán Graphs with Respect to the Number of Colorings SIAM J. Discret. Math. (IF 0.8) Pub Date : 2023-10-25 Melissa M. Fuentes
SIAM Journal on Discrete Mathematics, Volume 37, Issue 4, Page 2523-2543, December 2023. Abstract. We consider a problem proposed by Linial and Wilf to determine the structure of graphs that allows the maximum number of [math]-colorings among graphs with [math] vertices and [math] edges. Let [math] denote the Turán graph—the complete [math]-partite graph on [math] vertices with partition sizes as equal
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Edges Not Covered by Monochromatic Bipartite Graph SIAM J. Discret. Math. (IF 0.8) Pub Date : 2023-10-20 Xiutao Zhu, Ervin Györi, Zhen He, Zequn Lv, Nika Salia, Casey Tompkins, Kitti Varga
SIAM Journal on Discrete Mathematics, Volume 37, Issue 4, Page 2508-2522, December 2023. Abstract. Let [math] denote the maximum number of edges not contained in any monochromatic copy of [math] in a [math]-coloring of the edges of [math], and let [math] denote the Turán number of [math]. In place of [math] we simply write [math]. Keevash and Sudakov proved that [math] if [math] is an edge-critical
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The Fractional Chromatic Number of [math]-Free Graphs SIAM J. Discret. Math. (IF 0.8) Pub Date : 2023-10-19 Xiaolan Hu, Xing Peng
SIAM Journal on Discrete Mathematics, Volume 37, Issue 4, Page 2486-2507, December 2023. Abstract. For a simple graph [math], let [math] be the fractional chromatic number of [math]. In this paper, we aim to establish upper bounds on [math] for those graphs [math] with restrictions on the clique number. Namely, we prove that for [math], if [math] has maximum degree at most [math] and is [math]-free