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  • Topological Bounds for Graph Representations over Any Field
    SIAM J. Discret. Math. (IF 0.75) Pub Date : 2021-01-13
    Meysam Alishahi; Frédéric Meunier

    SIAM Journal on Discrete Mathematics, Volume 35, Issue 1, Page 91-104, January 2021. Haviv [European J. Combin., 81 (2019), pp. 84--97] has recently proved that some topological lower bounds on the chromatic number of graphs are also lower bounds on their orthogonality dimension over $\mathbb{R}$. We show that this actually holds for all known topological lower bounds and all fields. We also improve

    更新日期:2021-01-14
  • Graph Classes and Forbidden Patterns on Three Vertices
    SIAM J. Discret. Math. (IF 0.75) Pub Date : 2021-01-07
    Laurent Feuilloley; Michel Habib

    SIAM Journal on Discrete Mathematics, Volume 35, Issue 1, Page 55-90, January 2021. This paper deals with the characterization and the recognition of graph classes. A popular way to characterize a graph class is to list a minimal set of forbidden induced subgraphs. Unfortunately, this strategy rarely leads to a very efficient recognition algorithm. On the other hand, many graph classes can be efficiently

    更新日期:2021-01-08
  • On the Vanishing of Discrete Singular Cubical Homology for Graphs
    SIAM J. Discret. Math. (IF 0.75) Pub Date : 2021-01-07
    Hélène Barcelo; Curtis Greene; Abdul Salam Jarrah; Volkmar Welker

    SIAM Journal on Discrete Mathematics, Volume 35, Issue 1, Page 35-54, January 2021. We prove that if $G$ is a graph without 3-cycles and 4-cycles, then the discrete cubical homology of $G$ is trivial in dimension $d$ for all $d\ge 2$. We also construct a sequence $\{G_d\}$ of graphs such that this homology is nontrivial in dimension $d$ for $d\ge 1$. Finally, we show that the discrete cubical homology

    更新日期:2021-01-08
  • Ramsey Numbers Involving Large Books
    SIAM J. Discret. Math. (IF 0.75) Pub Date : 2021-01-05
    Qizhong Lin; Xiudi Liu

    SIAM Journal on Discrete Mathematics, Volume 35, Issue 1, Page 23-34, January 2021. The notion of goodness for Ramsey numbers was introduced by Burr and Erdös in 1983. For graphs $G$ and $H$, let $G+H$ be the graph obtained from disjoint $G$ and $H$ by adding all edges between the vertices of $G$ and $H$. Denote $nH$ by the union of $n$ disjoint copies of $H$. Let $B_n^{(k)}=K_k+nK_1$, which is called

    更新日期:2021-01-05
  • Improved Randomized Algorithm for k-Submodular Function Maximization
    SIAM J. Discret. Math. (IF 0.75) Pub Date : 2021-01-05
    Hiroki Oshima

    SIAM Journal on Discrete Mathematics, Volume 35, Issue 1, Page 1-22, January 2021. Submodularity is one of the most important properties in combinatorial optimization, and $k$-submodularity is a generalization of submodularity. Maximization of a $k$-submodular function requires an exponential number of value oracle queries, and approximation algorithms have been studied. For unconstrained $k$-submodular

    更新日期:2021-01-05
  • Erratum: The Bollobás--Scott Conjecture for 4-Uniform Hypergraphs
    SIAM J. Discret. Math. (IF 0.75) Pub Date : 2020-12-18
    Jianfeng Hou; Shufei Wu; Qinghou Zeng; Wenxing Zhu

    SIAM Journal on Discrete Mathematics, Volume 34, Issue 4, Page 2583-2584, January 2020. We are indebted to Spink and Tiba Spink and Tiba [3] for pointing out that the key technical lemma (Lemma 4) is incorrect in our paper [2]. We tried to make a revision for fixing the gap. However, with the help of mathematical software Lingo, we found that our lemma has counterexamples and its conclusion is incorrect

    更新日期:2020-12-20
  • On the Number of Cliques in Graphs with a Forbidden Subdivision or Immersion
    SIAM J. Discret. Math. (IF 0.75) Pub Date : 2020-12-15
    Jacob Fox; Fan Wei

    SIAM Journal on Discrete Mathematics, Volume 34, Issue 4, Page 2556-2582, January 2020. How many cliques can a graph on $n$ vertices have with a forbidden substructure? Extremal problems of this sort have been studied for a long time. This paper studies the maximum possible number of cliques in a graph on $n$ vertices with a forbidden clique subdivision or immersion. We prove for $t$ sufficiently large

    更新日期:2020-12-15
  • A Large Gap in a Dilate of a Set
    SIAM J. Discret. Math. (IF 0.75) Pub Date : 2020-12-10
    George Shakan

    SIAM Journal on Discrete Mathematics, Volume 34, Issue 4, Page 2553-2555, January 2020. Let $A \subset \mathbb{F}_p$ with $|A| > 1$. We show there is a $d \in \mathbb{F}_p^{\times}$ such that $d \cdot A$ contains a gap of size at least $2p/ |A| - 2 $.

    更新日期:2020-12-11
  • Large Homogeneous Submatrices
    SIAM J. Discret. Math. (IF 0.75) Pub Date : 2020-12-10
    Dániel Korándi; János Pach; István Tomon

    SIAM Journal on Discrete Mathematics, Volume 34, Issue 4, Page 2532-2552, January 2020. A matrix is homogeneous if all of its entries are equal. Let $P$ be a $2\times 2$ zero-one matrix that is not homogeneous. We prove that if an $n\times n$ zero-one matrix $A$ does not contain $P$ as a submatrix, then $A$ has a $cn\times cn$ homogeneous submatrix for a suitable constant $c>0$. We further provide

    更新日期:2020-12-11
  • Solutions to the Minimum Variance Problem Using Delaunay Triangulation
    SIAM J. Discret. Math. (IF 0.75) Pub Date : 2020-12-08
    Alexander Strang

    SIAM Journal on Discrete Mathematics, Volume 34, Issue 4, Page 2510-2531, January 2020. We consider the problem of minimizing the variance of a distribution supported on a finite set of points $\Omega$ in $\mathbb{R}^n$ given the expected value of the distribution. This produces the distribution with the least uncertainty in $X$, in the $l_2$ sense, given the support and the mean. We show that, for

    更新日期:2020-12-09
  • The Spherical Kakeya Problem in Finite Fields
    SIAM J. Discret. Math. (IF 0.75) Pub Date : 2020-12-08
    Mehdi Makhul; Audie Warren; Arne Winterhof

    SIAM Journal on Discrete Mathematics, Volume 34, Issue 4, Page 2502-2509, January 2020. We study subsets of the $n$-dimensional vector space over the finite field $\mathbb{F}_q$, for odd $q$, which contain either a sphere for each radius or a sphere for each first coordinate of the center. We call such sets radii spherical Kakeya sets and center spherical Kakeya sets, respectively. For $n\ge 4$ we

    更新日期:2020-12-09
  • On the Voronoi Conjecture for Combinatorially Voronoi Parallelohedra in Dimension 5
    SIAM J. Discret. Math. (IF 0.75) Pub Date : 2020-12-03
    Mathieu Dutour Sikirić; Alexey Garber; Alexander Magazinov

    SIAM Journal on Discrete Mathematics, Volume 34, Issue 4, Page 2481-2501, January 2020. In a recent paper, Garber, Gavrilyuk, and Magazinov [Discrete Comput. Geom., 53 (2015), pp. 245--260] proposed a sufficient combinatorial condition for a parallelohedron to be affinely Voronoi. We show that this condition holds for all 5-dimensional Voronoi parallelohedra. Consequently, the Voronoi conjecture in

    更新日期:2020-12-04
  • A Topologically Complete Theory of Weaving
    SIAM J. Discret. Math. (IF 0.75) Pub Date : 2020-11-24
    Ergun Akleman; Jianer Chen; Jonathan L. Gross; Shiyu Hu

    SIAM Journal on Discrete Mathematics, Volume 34, Issue 4, Page 2457-2480, January 2020. Recent advances in the computer graphics of woven images in 3-space motivate the development of a model for weavings on arbitrary surfaces of higher genus. Our paradigm differs markedly from what Grünbaum and Shepard have provided for the plane. In particular, we induce our weavings from graph imbeddings on surfaces

    更新日期:2020-11-25
  • On Generalized Perfect Difference Sumsets
    SIAM J. Discret. Math. (IF 0.75) Pub Date : 2020-11-18
    Jin-Hui Fang

    SIAM Journal on Discrete Mathematics, Volume 34, Issue 4, Page 2448-2456, January 2020. Let $\mathbb{Z}$ be the set of integers and $\mathbb{N}$ be the set of positive integers. For a nonempty set $A$ of integers and any integers $n$, $h\ge 2$, denote $r_{A,h}(n)$ by the number of representations of $n$ of the form $n=a_1+a_2+\cdots+a_h$, where $a_1\le \cdots \le a_h$ and $a_i\in A$ for $i=1,2,\ldots

    更新日期:2020-11-19
  • Hajós-Type Constructions and Neighborhood Complexes
    SIAM J. Discret. Math. (IF 0.75) Pub Date : 2020-11-18
    Benjamin Braun; Julianne Vega

    SIAM Journal on Discrete Mathematics, Volume 34, Issue 4, Page 2424-2447, January 2020. Any graph $G$ with chromatic number $k$ can be obtained using a Hajós-type construction, i.e., by iteratively performing the Hajós merge and vertex identification operations on a sequence of graphs starting with $K_k$. Finding such constructions for a given graph or family of graphs is a challenging task. In this

    更新日期:2020-11-19
  • Repeated Minimizers of $p$-Frame Energies
    SIAM J. Discret. Math. (IF 0.75) Pub Date : 2020-11-18
    Alexey Glazyrin; Josiah Park

    SIAM Journal on Discrete Mathematics, Volume 34, Issue 4, Page 2411-2423, January 2020. For a collection of $N$ unit vectors ${X}=\{x_i\}_{i=1}^N$, define the $p$-frame energy of ${X}$ as the quantity $\sum_{i\neq j} |\langle x_i,x_j \rangle|^p$. In this paper, we connect the problem of minimizing this value to another optimization problem, thus giving new lower bounds for such energies. In particular

    更新日期:2020-11-19
  • Counting Partitions inside a Rectangle
    SIAM J. Discret. Math. (IF 0.75) Pub Date : 2020-11-18
    Stephen Melczer; Greta Panova; Robin Pemantle

    SIAM Journal on Discrete Mathematics, Volume 34, Issue 4, Page 2388-2410, January 2020. We consider the number of partitions of $n$ whose Young diagrams fit inside an $m \times \ell$ rectangle; equivalently, we study the coefficients of the $q$-binomial coefficient $\binom{m+\ell}{m}_q$. We obtain sharp asymptotics throughout the regime $\ell = \Theta (m)$ and $n = \Theta (m^2)$, while previously sharp

    更新日期:2020-11-19
  • A Parametric Version of LLL and Some Consequences: Parametric Shortest and Closest Vector Problems
    SIAM J. Discret. Math. (IF 0.75) Pub Date : 2020-11-12
    Tristram Bogart; John Goodrick; Kevin Woods

    SIAM Journal on Discrete Mathematics, Volume 34, Issue 4, Page 2363-2387, January 2020. Given a parametric lattice with a basis given by polynomials in $\Bbb{Z}[t]$, we give an algorithm to construct an LLL-reduced basis whose elements are eventually quasi-polynomial in $t$: that is, they are given by formulas that are piecewise polynomial in $t$ (for sufficiently large $t$), such that each piece is

    更新日期:2020-11-13
  • Anti-Ramsey Number of Edge-Disjoint Rainbow Spanning Trees
    SIAM J. Discret. Math. (IF 0.75) Pub Date : 2020-11-12
    Linyuan Lu; Zhiyu Wang

    SIAM Journal on Discrete Mathematics, Volume 34, Issue 4, Page 2346-2362, January 2020. An edge-colored graph $G$ is called rainbow if every edge of $G$ receives a different color. The anti-Ramsey number of $t$ edge-disjoint rainbow spanning trees, denoted by $r(n,t)$, is defined as the maximum number of colors in an edge-coloring of $K_n$ containing no $t$ edge-disjoint rainbow spanning trees. Jahanbekam

    更新日期:2020-11-13
  • New Turán Exponents for Two Extremal Hypergraph Problems
    SIAM J. Discret. Math. (IF 0.75) Pub Date : 2020-11-09
    Chong Shangguan; Itzhak Tamo

    SIAM Journal on Discrete Mathematics, Volume 34, Issue 4, Page 2338-2345, January 2020. An $r$-uniform hypergraph is called $t$-cancellative if for any $t+2$ distinct edges $A_1,\ldots,A_t,B,C$, it holds that $(\cup_{i=1}^t A_i)\cup B\neq (\cup_{i=1}^t A_i)\cup C$. It is called $t$-union-free if for any two distinct subsets $\mathcal{A}, \mathcal{B}$, each consisting of at most $t$ edges, it holds

    更新日期:2020-11-12
  • Efficiently Realizing Interval Sequences
    SIAM J. Discret. Math. (IF 0.75) Pub Date : 2020-11-09
    Amotz Bar-Noy; Keerti Choudhary; David Peleg; Dror Rawitz

    SIAM Journal on Discrete Mathematics, Volume 34, Issue 4, Page 2318-2337, January 2020. We consider the problem of realizable interval sequences. An interval sequence is comprised of $n$ integer intervals $[a_i,b_i]$ such that $0\le a_i\leq b_i \le n-1$ and is said to be graphic/realizable if there exists a graph with degree sequence, say, $D=(d_1,\ldots,d_n),$ satisfying the condition $a_i\leq d_i\leq

    更新日期:2020-11-12
  • Binary Linear Codes with Near-Extremal Maximum Distance
    SIAM J. Discret. Math. (IF 0.75) Pub Date : 2020-11-09
    András Pongrácz

    SIAM Journal on Discrete Mathematics, Volume 34, Issue 4, Page 2300-2317, January 2020. Let $C$ denote a binary linear code with length $n$ all of whose coordinates are essential; i.e., for each coordinate there is a codeword that is not zero in that position. Then the maximum distance $D$ is strictly bigger than $n/2$, and the extremum $D=(n+1)/2$ is attained exactly by punctured Hadamard codes. In

    更新日期:2020-11-12
  • Near-Linear Time Algorithm for $n$-Fold ILPs via Color Coding
    SIAM J. Discret. Math. (IF 0.75) Pub Date : 2020-11-03
    Klaus Jansen; Alexandra Lassota; Lars Rohwedder

    SIAM Journal on Discrete Mathematics, Volume 34, Issue 4, Page 2282-2299, January 2020. We study an important case of integer linear programs (ILPs) of the form $\max\{c^Tx \ \vert\ \mathcal Ax = b, l \leq x \leq u,\, x \in \mathbb{Z}^{n t} \} $ with $n t$ variables and lower and upper bounds $\ell, u\in\mathbb Z^{nt}$. In $n$-fold ILPs nonzero entries only appear in the first $r$ rows of the matrix

    更新日期:2020-11-04
  • A Ramsey Theorem for Biased Graphs
    SIAM J. Discret. Math. (IF 0.75) Pub Date : 2020-11-03
    Peter Nelson; Sophia Park

    SIAM Journal on Discrete Mathematics, Volume 34, Issue 4, Page 2270-2281, January 2020. A biased graph is a pair $(G,\mathcal{B})$, where $G$ is a graph and $\mathcal{B}$ is a collection of “balanced” cycles of $G$ such that no $\Theta$-subgraph of $G$ contains precisely two balanced cycles. We prove a Ramsey-type theorem, showing that if $(G,\mathcal{B})$ is a biased graph for which $G$ is a very

    更新日期:2020-11-04
  • Coloring Hypergraphs Defined by Stabbed Pseudo-Disks and ABAB-Free Hypergraphs
    SIAM J. Discret. Math. (IF 0.75) Pub Date : 2020-11-02
    Eyal Ackerman; Balázs Keszegh; Dömötör Pálvölgyi

    SIAM Journal on Discrete Mathematics, Volume 34, Issue 4, Page 2250-2269, January 2020. What is the minimum number of colors that always suffice to color every planar set of points such that any disk that contains enough points contains two points of different colors? It is known that the answer to this question is either three or four. We show that three colors always suffice if the condition must

    更新日期:2020-11-02
  • Improved Bound for Tomaszewski's Problem
    SIAM J. Discret. Math. (IF 0.75) Pub Date : 2020-11-02
    Vojtech Dvorak; Peter van Hintum; Marius Tiba

    SIAM Journal on Discrete Mathematics, Volume 34, Issue 4, Page 2239-2249, January 2020. In 1986, Tomaszewski made the following conjecture. Given $n$ real numbers $a_{1},\ldots,a_{n}$ with $\sum_{i=1}^{n}a_{i}^{2}=1$, then of the $2^{n}$ signed sums $\pm a_{1} \pm \cdots \pm a_{n}$, at least half have absolute value at most 1. Hendriks and van Zuijlen [An Improvement of the Boppana-Holzman Bound for

    更新日期:2020-11-02
  • Progress on the Adjacent Vertex Distinguishing Edge Coloring Conjecture
    SIAM J. Discret. Math. (IF 0.75) Pub Date : 2020-11-02
    Gwenaël Joret; William Lochet

    SIAM Journal on Discrete Mathematics, Volume 34, Issue 4, Page 2221-2238, January 2020. A proper edge coloring of a graph is adjacent vertex distinguishing if no two adjacent vertices see the same set of colors. Using a clever application of the local lemma, Hatami [J. Combin. Theory Ser. B, 95 (2005), pp. 246--256] proved that every graph with maximum degree $\Delta$ and no isolated edge has an adjacent

    更新日期:2020-11-02
  • Erdös--Falconer Distance Problem under Hamming Metric in Vector Spaces over Finite Fields
    SIAM J. Discret. Math. (IF 0.75) Pub Date : 2020-11-02
    Zixiang Xu; Gennian Ge

    SIAM Journal on Discrete Mathematics, Volume 34, Issue 4, Page 2208-2220, January 2020. For a subset $I\subseteq \mathbb{F}_{q}^{n}$, let $\Delta(I)$ be the set of distances determined by the elements of $I.$ The Erdös--Falconer distance problem in $\mathbb{F}_{q}^{n}$ asks for a threshold on the cardinality $|I|$ so that $\Delta(I)$ contains a positive proportion of the whole distance set. In this

    更新日期:2020-11-02
  • Minimum Violation Vertex Maps and Their Applications to Cut Problems
    SIAM J. Discret. Math. (IF 0.75) Pub Date : 2020-10-22
    Ken-ichi Kawarabayashi; Chao Xu

    SIAM Journal on Discrete Mathematics, Volume 34, Issue 4, Page 2183-2207, January 2020. The minimum violation problem asks for a vertex map from a digraph to a pattern digraph that minimizes violation, the total weight of the edges not mapped to an edge. We are interested in surjective mappings. We characterize all patterns where a minimum violation map that fixes some vertices can be computed in polynomial

    更新日期:2020-10-26
  • Flows on Signed Graphs without Long Barbells
    SIAM J. Discret. Math. (IF 0.75) Pub Date : 2020-10-20
    You Lu; Rong Luo; Michael Schubert; Eckhard Steffen; Cun-Quan Zhang

    SIAM Journal on Discrete Mathematics, Volume 34, Issue 4, Page 2166-2182, January 2020. Many basic properties in Tutte's flow theory for unsigned graphs do not have their counterparts for signed graphs. However, signed graphs without long barbells in many ways behave like unsigned graphs from the point view of flows. In this paper, we study whether some basic properties in Tutte's flow theory remain

    更新日期:2020-10-26
  • $(3a:a)$-List-Colorability of Embedded Graphs of Girth at Least Five
    SIAM J. Discret. Math. (IF 0.75) Pub Date : 2020-10-20
    Zdeněk Dvořák; Xiaolan Hu

    SIAM Journal on Discrete Mathematics, Volume 34, Issue 4, Page 2137-2165, January 2020. A graph $G$ is list $(b:a)$-colorable if for every assignment of lists of size $b$ to vertices of $G$ there exists a choice of an $a$-element subset of the list at each vertex such that the subsets chosen at adjacent vertices are disjoint. We prove that for every positive integer $a$, the family of minimal obstructions

    更新日期:2020-10-26
  • Bounds of Trilinear and Trinomial Exponential Sums
    SIAM J. Discret. Math. (IF 0.75) Pub Date : 2020-10-19
    Simon Macourt; Giorgis Petridis; Ilya D. Shkredov; Igor E. Shparlinski

    SIAM Journal on Discrete Mathematics, Volume 34, Issue 4, Page 2124-2136, January 2020. We prove, for a sufficiently small subset $\mathcal{A}$ of a prime residue field, an estimate on the number of solutions to the equation $(a_1-a_2)(a_3-a_4) = (a_5-a_6)(a_7-a_8)$ with all variables in $\mathcal{A}$. We then derive new bounds on trilinear exponential sums and on the total number of residues equaling

    更新日期:2020-10-19
  • Maximum and Minimum Degree Conditions for Embedding Trees
    SIAM J. Discret. Math. (IF 0.75) Pub Date : 2020-10-13
    Guido Besomi; Matías Pavez-Signé; Maya Stein

    SIAM Journal on Discrete Mathematics, Volume 34, Issue 4, Page 2108-2123, January 2020. We propose the following conjecture: For every fixed $\alpha\in [0,\frac 13)$, each graph of minimum degree at least $(1+\alpha)\frac k2$ and maximum degree at least $2(1-\alpha)k$ contains each tree with $k$ edges as a subgraph. Our main result is an approximate version of the conjecture for bounded degree trees

    更新日期:2020-10-13
  • Rerouting Flows when Links Fail
    SIAM J. Discret. Math. (IF 0.75) Pub Date : 2020-10-13
    Jannik Matuschke; S. Thomas McCormick; Gianpaolo Oriolo

    SIAM Journal on Discrete Mathematics, Volume 34, Issue 4, Page 2082-2107, January 2020. We introduce reroutable flows, a robust version of network flows in which link failures can be mitigated by rerouting the affected flow. An important new feature of this model, distinguishing it from existing robust network flow models, is that no flow can get lost in the network. Our goal is to compute maximum

    更新日期:2020-10-13
  • Resolvability of Hamming Graphs
    SIAM J. Discret. Math. (IF 0.75) Pub Date : 2020-10-08
    Lucas Laird; Richard C. Tillquist; Stephen Becker; Manuel E. Lladser

    SIAM Journal on Discrete Mathematics, Volume 34, Issue 4, Page 2063-2081, January 2020. A subset of vertices in a graph is called resolving when the geodesic distances to those vertices uniquely distinguish every vertex in the graph. Here, we characterize the resolvability of Hamming graphs in terms of a constrained linear system and deduce a novel but straightforward characterization of resolvability

    更新日期:2020-10-11
  • Subcritical Random Hypergraphs, High-Order Components, and Hypertrees
    SIAM J. Discret. Math. (IF 0.75) Pub Date : 2020-10-08
    Oliver Cooley; Wenjie Fang; Nicola Del Giudice; Mihyun Kang

    SIAM Journal on Discrete Mathematics, Volume 34, Issue 4, Page 2033-2062, January 2020. One of the central topics in the theory of random graphs deals with the phase transition in the order of the largest components. In the binomial random graph $\mathcal{G}(n,p)$, the threshold for the appearance of the unique largest component (also known as the giant component) is $p_g = n^{-1}$. More precisely

    更新日期:2020-10-11
  • Few Sequence Pairs Suffice: Representing All Rectangle Placements
    SIAM J. Discret. Math. (IF 0.75) Pub Date : 2020-10-01
    Jannik Silvanus; Jens Vygen

    SIAM Journal on Discrete Mathematics, Volume 34, Issue 4, Page 2017-2032, January 2020. We consider representations of general nonoverlapping placements of rectangles by spatial relations (west, south, east, north) of pairs of rectangles. We call a set of representations complete if it contains a representation of every placement of $n$ rectangles. We prove a new upper bound of $\mathcal{O}(\frac{n

    更新日期:2020-10-02
  • A Short Note on Open-Neighborhood Conflict-Free Colorings of Graphs
    SIAM J. Discret. Math. (IF 0.75) Pub Date : 2020-09-24
    Fei Huang; Shanshan Guo; Jinjiang Yuan

    SIAM Journal on Discrete Mathematics, Volume 34, Issue 3, Page 2009-2015, January 2020. A graph is said to be open-neighborhood conflict-free $k$-colorable if there exists an assignment of $k$ different colors to some of the vertices such that, for every vertex $v$, there is a color that is assigned to exactly one vertex among the neighbors of $v$. The open-neighborhood conflict-free chromatic number

    更新日期:2020-09-25
  • Color Isomorphic Even Cycles and a Related Ramsey Problem
    SIAM J. Discret. Math. (IF 0.75) Pub Date : 2020-09-24
    Gennian Ge; Yifan Jing; Zixiang Xu; Tao Zhang

    SIAM Journal on Discrete Mathematics, Volume 34, Issue 3, Page 1999-2008, January 2020. In this paper, we first study a new extremal problem recently posed by Conlon and Tyomkyn [Repeated Patterns in Proper Colourings, preprint, https://arxiv.org/abs/2002.00921 (2020)]. Given a graph $H$ and an integer $k\geqslant 2$, let $f_{k}(n,H)$ be the smallest number of colors $c$ such that there exists a proper

    更新日期:2020-09-24
  • Growth in Some Finite Three-Dimensional Matrix Groups
    SIAM J. Discret. Math. (IF 0.75) Pub Date : 2020-09-23
    Brendan Murphy; James Wheeler

    SIAM Journal on Discrete Mathematics, Volume 34, Issue 3, Page 1984-1998, January 2020. We study the growth of product sets in some finite three-dimensional matrix groups. In particular, we prove two results about the group of $2\times 2$ upper triangular matrices over arbitrary finite fields: a product set estimate using techniques from multiplicative combinatorics and an energy estimate using incidence

    更新日期:2020-09-23
  • Bipartite Analogues of Comparability and Cocomparability Graphs
    SIAM J. Discret. Math. (IF 0.75) Pub Date : 2020-09-15
    Pavol Hell; Jing Huang; Jephian C.-H. Lin; Ross M. McConnell

    SIAM Journal on Discrete Mathematics, Volume 34, Issue 3, Page 1969-1983, January 2020. We propose bipartite analogues of comparability and cocomparability graphs. Surprisingly, the two classes coincide. We call these bipartite graphs cocomparability bigraphs. We characterize cocomparability bigraphs in terms of vertex orderings, forbidden substructures, and orientations of their complements. In particular

    更新日期:2020-09-15
  • Invariants of Rational Links Represented by Reduced Alternating Diagrams
    SIAM J. Discret. Math. (IF 0.75) Pub Date : 2020-09-15
    Yuanan Diao; Claus Ernst; Gábor Hetyei

    SIAM Journal on Discrete Mathematics, Volume 34, Issue 3, Page 1944-1968, January 2020. A rational link may be represented by any of the (infinitely) many link diagrams corresponding to various continued fraction expansions of the same rational number. The continued fraction expansion of the rational number in which all signs are the same is called a nonalternating form, and the diagram corresponding

    更新日期:2020-09-15
  • Extremal Theory of Locally Sparse Multigraphs
    SIAM J. Discret. Math. (IF 0.75) Pub Date : 2020-09-09
    Dhruv Mubayi; Caroline Terry

    SIAM Journal on Discrete Mathematics, Volume 34, Issue 3, Page 1922-1943, January 2020. An $(n,s,q)$-graph is an $n$-vertex multigraph where every set of $s$ vertices spans at most $q$ edges. In this paper, we determine the maximum product of the edge multiplicities in $(n,s,q)$-graphs if the congruence class of $q$ modulo ${s\choose 2}$ is in a certain interval of length about $3s/2$. The smallest

    更新日期:2020-09-10
  • Subgroup Perfect Codes in Cayley Graphs
    SIAM J. Discret. Math. (IF 0.75) Pub Date : 2020-09-01
    Xuanlong Ma; Gary L. Walls; Kaishun Wang; Sanming Zhou

    SIAM Journal on Discrete Mathematics, Volume 34, Issue 3, Page 1909-1921, January 2020. Let $\Gamma$ be a graph with vertex set $V(\Gamma)$. A subset $C$ of $V(\Gamma)$ is called a perfect code in $\Gamma$ if $C$ is an independent set of $\Gamma$ and every vertex in $V(\Gamma)\setminus C$ is adjacent to exactly one vertex in $C$. A subset $C$ of a group $G$ is called a perfect code of $G$ if there

    更新日期:2020-09-01
  • Ramsey Goodness of Cycles
    SIAM J. Discret. Math. (IF 0.75) Pub Date : 2020-09-01
    Alexey Pokrovskiy; Benny Sudakov

    SIAM Journal on Discrete Mathematics, Volume 34, Issue 3, Page 1884-1908, January 2020. Given a pair of graphs $G$ and $H$, the Ramsey number $R(G,H)$ is the smallest $N$ such that every red-blue coloring of the edges of the complete graph $K_N$ contains a red copy of $G$ or a blue copy of $H$. If a graph $G$ is connected, it is well known and easy to show that $R(G,H) \geq (|G|-1)(\chi(H)-1)+\sigma(H)$

    更新日期:2020-09-01
  • Tight Hardness Results for Consensus Problems on Circular Strings and Time Series
    SIAM J. Discret. Math. (IF 0.75) Pub Date : 2020-08-25
    Laurent Bulteau; Vincent Froese; Rolf Niedermeier

    SIAM Journal on Discrete Mathematics, Volume 34, Issue 3, Page 1854-1883, January 2020. Consensus problems for strings and sequences appear in numerous application contexts, ranging from bioinformatics to data mining to machine learning. Closing some gaps in the literature, we show that several fundamental problems in this context are NP- and W[1]-hard and that the known (including some brute-force)

    更新日期:2020-08-26
  • $k$-Arrangements, Statistics, and Patterns
    SIAM J. Discret. Math. (IF 0.75) Pub Date : 2020-08-24
    Shishuo Fu; Guo-Niu Han; Zhicong Lin

    SIAM Journal on Discrete Mathematics, Volume 34, Issue 3, Page 1830-1853, January 2020. The $k$-arrangements are permutations whose fixed points are $k$-colored. We prove enumerative results related to statistics and patterns on $k$-arrangements, confirming several conjectures by Blitvić and Steingrímsson. In particular, one of their conjectures regarding the equidistribution of the number of descents

    更新日期:2020-08-25
  • $t$-Wise Berge and $t$-Heavy Hypergraphs
    SIAM J. Discret. Math. (IF 0.75) Pub Date : 2020-08-20
    Dániel Gerbner; Dániel T. Nagy; Balázs Patkós; Máté Vizer

    SIAM Journal on Discrete Mathematics, Volume 34, Issue 3, Page 1813-1829, January 2020. In many proofs concerning extremal parameters of Berge hypergraphs one starts with analyzing that part of that shadow graph which is contained in many hyperedges. Capturing this phenomenon we introduce two new types of hypergraphs. A hypergraph ${\mathcal H}$ is a $t$-heavy copy of a graph $F$ if there is a copy

    更新日期:2020-08-20
  • Dynamic Balanced Graph Partitioning
    SIAM J. Discret. Math. (IF 0.75) Pub Date : 2020-08-12
    Chen Avin; Marcin Bienkowski; Andreas Loukas; Maciej Pacut; Stefan Schmid

    SIAM Journal on Discrete Mathematics, Volume 34, Issue 3, Page 1791-1812, January 2020. This paper initiates the study of the classic balanced graph partitioning problem from an online perspective: Given an arbitrary sequence of pairwise communication requests between $n$ nodes, with patterns that may change over time, the objective is to service these requests efficiently by partitioning the nodes

    更新日期:2020-08-14
  • Birkhoff--von Neumann Graphs that are PM-Compact
    SIAM J. Discret. Math. (IF 0.75) Pub Date : 2020-08-12
    Marcelo H. De Carvalho; Nishad Kothari; Xiumei Wang; Yixun Lin

    SIAM Journal on Discrete Mathematics, Volume 34, Issue 3, Page 1769-1790, January 2020. A well-studied geometric object in combinatorial optimization is the perfect matching polytope of a graph $G$---the convex hull of the incidence vectors of all perfect matchings of $G$. In any investigation concerning the perfect matching polytope, one may assume that $G$ is matching covered---that is, $G$ is a

    更新日期:2020-08-14
  • Sparse Graphs Are Near-Bipartite
    SIAM J. Discret. Math. (IF 0.75) Pub Date : 2020-08-11
    Daniel W. Cranston; Matthew P. Yancey

    SIAM Journal on Discrete Mathematics, Volume 34, Issue 3, Page 1725-1768, January 2020. A multigraph $G$ is near-bipartite if $V(G)$ can be partitioned as $I,F$ such that $I$ is an independent set and $F$ induces a forest. We prove that a multigraph $G$ is near-bipartite when $3|W|-2|E(G[W])|\ge -1$ for every $W\subseteq V(G)$, and $G$ contains no $K_4$ and no Moser spindle. We prove that a simple

    更新日期:2020-08-14
  • Min-Orderable Digraphs
    SIAM J. Discret. Math. (IF 0.75) Pub Date : 2020-08-03
    Pavol Hell; Jing Huang; Ross M. McConnell; Arash Rafiey

    SIAM Journal on Discrete Mathematics, Volume 34, Issue 3, Page 1710-1724, January 2020. We unify several seemingly different graph and digraph classes under one umbrella. These classes are all, broadly speaking, different generalizations of interval graphs, and include, in addition to interval graphs, adjusted interval digraphs, complements of threshold tolerance graphs (known as co-TT graphs), bipartite

    更新日期:2020-08-04
  • Minor-Closed Graph Classes with Bounded Layered Pathwidth
    SIAM J. Discret. Math. (IF 0.75) Pub Date : 2020-07-30
    Vida Dujmović; David Eppstein; Gwenaël Joret; Pat Morin; David R. Wood

    SIAM Journal on Discrete Mathematics, Volume 34, Issue 3, Page 1693-1709, January 2020. We prove that a minor-closed class of graphs has bounded layered pathwidth if and only if some apex-forest is not in the class. This generalizes a theorem of Robertson and Seymour, which says that a minor-closed class of graphs has bounded pathwidth if and only if some forest is not in the class.

    更新日期:2020-07-31
  • A Rainbow Dirac's Theorem
    SIAM J. Discret. Math. (IF 0.75) Pub Date : 2020-07-30
    Matthew Coulson; Guillem Perarnau

    SIAM Journal on Discrete Mathematics, Volume 34, Issue 3, Page 1670-1692, January 2020. A famous theorem of Dirac states that any graph on $n$ vertices with minimum degree at least $n/2$ has a Hamilton cycle. Such graphs are called Dirac graphs. Strengthening this result, we show the existence of rainbow Hamilton cycles in $\mu n$-bounded colorings of Dirac graphs for sufficiently small $\mu >0$.

    更新日期:2020-07-31
  • Breaking 1 - 1/e Barrier for Nonpreemptive Throughput Maximization
    SIAM J. Discret. Math. (IF 0.75) Pub Date : 2020-07-30
    Sungjin Im; Shi Li; Benjamin Moseley

    SIAM Journal on Discrete Mathematics, Volume 34, Issue 3, Page 1649-1669, January 2020. In this paper we consider one of the most basic scheduling problems where jobs have their respective arrival times and deadlines. The goal is to schedule as many jobs as possible nonpreemptively by their respective deadlines on $m$ identical parallel machines. For the last decade, the best approximation ratio known

    更新日期:2020-07-31
  • Hitting Minors on Bounded Treewidth Graphs. I. General Upper Bounds
    SIAM J. Discret. Math. (IF 0.75) Pub Date : 2020-07-29
    Julien Baste; Ignasi Sau; Dimitrios M. Thilikos

    SIAM Journal on Discrete Mathematics, Volume 34, Issue 3, Page 1623-1648, January 2020. For a finite collection of graphs ${\cal F}$, the $\mathcal{F}$-M-Deletion problem consists in, given a graph $G$ and an integer $k$, deciding whether there exists $S \subseteq V(G)$ with $|S| \leq k$ such that $G \setminus S$ does not contain any of the graphs in ${\cal F}$ as a minor. We are interested in the

    更新日期:2020-07-29
  • Order-Isomorphic Twins in Permutations
    SIAM J. Discret. Math. (IF 0.75) Pub Date : 2020-07-27
    Boris Bukh; Oleksandr Rudenko

    SIAM Journal on Discrete Mathematics, Volume 34, Issue 3, Page 1620-1622, January 2020. Let $a_1,\ldots,a_n$ be a permutation of $[n]$. Two disjoint order-isomorphic subsequences are called twins. We show that every permutation of $[n]$ contains twins of length $\Omega(n^{3/5})$ improving the trivial bound of $\Omega(n^{1/2})$. We also show that a random permutation contains twins of length $\Omega(n^{2/3})$

    更新日期:2020-07-27
  • Erdös--Pósa from Ball Packing
    SIAM J. Discret. Math. (IF 0.75) Pub Date : 2020-07-27
    Wouter Cames van Batenburg; Gwenaël Joret; Arthur Ulmer

    SIAM Journal on Discrete Mathematics, Volume 34, Issue 3, Page 1609-1619, January 2020. A classic theorem of Erdös and Pósa [Canad. J. Math., 17 (1965), pp. 347--352] states that every graph has either $k$ vertex-disjoint cycles or a set of $O(k \log k)$ vertices meeting all its cycles. While the standard proof revolves around finding a large “frame” in the graph (a subdivision of a large cubic graph)

    更新日期:2020-07-27
  • Minimal Cohen--Macaulay Simplicial Complexes
    SIAM J. Discret. Math. (IF 0.75) Pub Date : 2020-07-22
    Hailong Dao; Joseph Doolittle; Justin Lyle

    SIAM Journal on Discrete Mathematics, Volume 34, Issue 3, Page 1602-1608, January 2020. We define and study the notion of a minimal Cohen--Macaulay simplicial complex. We prove that any Cohen--Macaulay complex is shelled over a minimal one in our sense, and we give sufficient conditions for a complex to be minimal Cohen--Macaulay. We show that many interesting examples of Cohen--Macaulay complexes

    更新日期:2020-07-23
  • Going Far from Degeneracy
    SIAM J. Discret. Math. (IF 0.75) Pub Date : 2020-07-20
    Fedor V. Fomin; Petr A. Golovach; Daniel Lokshtanov; Fahad Panolan; Saket Saurabh; Meirav Zehavi

    SIAM Journal on Discrete Mathematics, Volume 34, Issue 3, Page 1587-1601, January 2020. An undirected graph $G$ is $d$-degenerate if every subgraph of $G$ has a vertex of degree at most $d$. By the classical theorem of Erdös and Gallai from 1959, every graph of degeneracy $d>1$ contains a cycle of length at least $d+1$. The proof of Erdös and Gallai is constructive and can be turned into a polynomial

    更新日期:2020-07-20
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