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  • When Do Envy-Free Allocations Exist?
    SIAM J. Discret. Math. (IF 0.75) Pub Date : 2020-07-02
    Pasin Manurangsi; Warut Suksompong

    SIAM Journal on Discrete Mathematics, Volume 34, Issue 3, Page 1505-1521, January 2020. We consider a fair division setting in which $m$ indivisible items are to be allocated among $n$ agents, where the agents have additive utilities and the agents' utilities for individual items are independently sampled from a distribution. Previous work has shown that an envy-free allocation is likely to exist when

    更新日期:2020-07-03
  • Sparse Hypergraphs with Applications to Coding Theory
    SIAM J. Discret. Math. (IF 0.75) Pub Date : 2020-07-02
    Chong Shangguan; Itzhak Tamo

    SIAM Journal on Discrete Mathematics, Volume 34, Issue 3, Page 1493-1504, January 2020. For fixed integers $r\ge 3,e\ge 3,v\ge r+1$, an $r$-uniform hypergraph is called $\mathscr{G}_r(v,e)$-free if the union of any $e$ distinct edges contains at least $v+1$ vertices. Brown, Erdös, and Sós showed that the maximum number of edges of such a hypergraph on $n$ vertices, denoted as $f_r(n,v,e)$, satisfies

    更新日期:2020-07-03
  • The Turán Number of Berge-$K_4$ in 3-Uniform Hypergraphs
    SIAM J. Discret. Math. (IF 0.75) Pub Date : 2020-07-01
    Hui Zhu; Liying Kang; Zhenyu Ni; Erfang Shan

    SIAM Journal on Discrete Mathematics, Volume 34, Issue 3, Page 1485-1492, January 2020. For a graph $G=(V,E)$, a hypergraph $H$ is called a Berge-$G$ if there is a bijection $f:E(G)\mapsto E(H)$ such that $e\subseteq f(e)$ for all $e\in E(G)$. The family of Berge-$G$ hypergraphs is denoted by $\mathcal{B}(G)$. The maximum number of edges in an $n$-vertex $r$-graph with no subhypergraph isomorphic to

    更新日期:2020-07-01
  • On the Maximum Weight Independent Set Problem in Graphs without Induced Cycles of Length at Least Five
    SIAM J. Discret. Math. (IF 0.75) Pub Date : 2020-06-29
    Maria Chudnovsky; Marcin Pilipczuk; Michał Pilipczuk; Stéphan Thomassé

    SIAM Journal on Discrete Mathematics, Volume 34, Issue 2, Page 1472-1483, January 2020. A hole in a graph is an induced cycle of length at least 4, and an antihole is the complement of an induced cycle of length at least 4. A hole or antihole is long if its length is at least 5. For an integer $k$, the $k$-prism is the graph consisting of two cliques of size $k$ joined by a matching. The complexity

    更新日期:2020-06-30
  • Partitioning Edge-Colored Hypergraphs into Few Monochromatic Tight Cycles
    SIAM J. Discret. Math. (IF 0.75) Pub Date : 2020-06-29
    Sebastián Bustamante; Jan Corsten; Nóra Frankl; Alexey Pokrovskiy; Jozef Skokan

    SIAM Journal on Discrete Mathematics, Volume 34, Issue 2, Page 1460-1471, January 2020. Confirming a conjecture of Gyárfás, we prove that, for all natural numbers $k$ and $r$, the vertices of every $r$-edge-colored complete $k$-uniform hypergraph can be partitioned into a bounded number (independent of the size of the hypergraph) of monochromatic tight cycles. We further prove that, for all natural

    更新日期:2020-06-30
  • Complexity of Two-dimensional Bootstrap Percolation Difficulty: Algorithm and NP-Hardness
    SIAM J. Discret. Math. (IF 0.75) Pub Date : 2020-06-29
    Ivailo Hartarsky; Tamás Róbert Mezei

    SIAM Journal on Discrete Mathematics, Volume 34, Issue 2, Page 1444-1459, January 2020. Bootstrap percolation is a class of cellular automata with random initial state. Two-dimensional bootstrap percolation models have three rough universality classes, the most studied being the “critical” one. For this class the scaling of the quantity of greatest interest (the critical probability) was determined

    更新日期:2020-06-30
  • Tight Analysis of the Smartstart Algorithm for Online Dial-a-Ride on the Line
    SIAM J. Discret. Math. (IF 0.75) Pub Date : 2020-06-22
    Alexander Birx; Yann Disser

    SIAM Journal on Discrete Mathematics, Volume 34, Issue 2, Page 1409-1443, January 2020. The online Dial-a-Ride problem is a fundamental online problem in a metric space, where transportation requests appear over time and may be served in any order by a single server with unit speed. Restricted to the real line, online Dial-a-Ride captures natural problems like controlling a personal elevator. Tight

    更新日期:2020-06-30
  • Odd Multiway Cut in Directed Acyclic Graphs
    SIAM J. Discret. Math. (IF 0.75) Pub Date : 2020-06-22
    Karthekeyan Chandrasekaran; Matthias Mnich; Sahand Mozaffari

    SIAM Journal on Discrete Mathematics, Volume 34, Issue 2, Page 1385-1408, January 2020. We investigate the odd multiway node (edge) cut problem where the input is a graph with a specified collection of terminal nodes, and the goal is to find a smallest subset of non-terminal nodes (edges) to delete so that the terminal nodes do not have an odd length path between them. In an earlier work, Lokshtanov

    更新日期:2020-06-30
  • Cops and Robbers on Graphs of Bounded Diameter
    SIAM J. Discret. Math. (IF 0.75) Pub Date : 2020-06-17
    Seyyed Aliasghar Hosseini; Fiachra Knox; Bojan Mohar

    SIAM Journal on Discrete Mathematics, Volume 34, Issue 2, Page 1375-1384, January 2020. The game of Cops and Robbers is a well-known game played on graphs. In this paper, we consider the class of graphs of bounded diameter. We improve the strategy of cops and the previously used probabilistic method, which results in an improved upper bound for the cop number of graphs of bounded diameter. In particular

    更新日期:2020-06-30
  • Extremal Graphs with Local Covering Conditions
    SIAM J. Discret. Math. (IF 0.75) Pub Date : 2020-06-16
    Debsoumya Chakraborti; Po-Shen Loh

    SIAM Journal on Discrete Mathematics, Volume 34, Issue 2, Page 1354-1374, January 2020. We systematically study a natural problem in extremal graph theory, to minimize the number of edges in a graph with a fixed number of vertices, subject to a certain local condition: each vertex must be in a copy of a fixed graph $H$. We completely solve this problem when $H$ is a clique, as well as more generally

    更新日期:2020-06-30
  • LP Relaxation and Tree Packing for Minimum $k$-Cut
    SIAM J. Discret. Math. (IF 0.75) Pub Date : 2020-06-16
    Chandra Chekuri; Kent Quanrud; Chao Xu

    SIAM Journal on Discrete Mathematics, Volume 34, Issue 2, Page 1334-1353, January 2020. Karger used spanning tree packings [D. R. Karger, J. ACM, 47 (2000), pp. 46--76] to derive a near linear-time randomized algorithm for the global minimum cut problem as well as a bound on the number of approximate minimum cuts. This is a different approach from his well-known random contraction algorithm [D. R.

    更新日期:2020-06-30
  • Regular Behavior of the Maximal Hypergraph Chromatic Number
    SIAM J. Discret. Math. (IF 0.75) Pub Date : 2020-06-15
    Danila Cherkashin; Fedor Petrov

    SIAM Journal on Discrete Mathematics, Volume 34, Issue 2, Page 1326-1333, January 2020. Let $m(n,r)$ denote the minimal number of edges in an $n$-uniform hypergraph which is not $r$-colorable. It is known that for a fixed $n$ one has $c_n r^n < m(n,r) < C_n r^n$. We prove that for any fixed $n$ the sequence $a_r := m(n,r)/r^n$ has a limit, which was conjectured by Alon. We also prove the list colorings

    更新日期:2020-06-30
  • Path Contraction Faster than $2^n$
    SIAM J. Discret. Math. (IF 0.75) Pub Date : 2020-06-11
    Akanksha Agrawal; Fedor V. Fomin; Daniel Lokshtanov; Saket Saurabh; Prafullkumar Tale

    SIAM Journal on Discrete Mathematics, Volume 34, Issue 2, Page 1302-1325, January 2020. A graph $G$ is contractible to a graph $H$ if there is a set $X \subseteq E(G)$, such that $G/X$ is isomorphic to $H$. Here, $G/X$ is the graph obtained from $G$ by contracting all the edges in $X$. For a family of graphs $\cal F$, the $\mathcal{F}$-Contraction problem takes as input a graph $G$ on $n$ vertices

    更新日期:2020-06-30
  • A Conjecture of Verstraëte on Vertex-Disjoint Cycles
    SIAM J. Discret. Math. (IF 0.75) Pub Date : 2020-06-11
    Jun Gao; Jie Ma

    SIAM Journal on Discrete Mathematics, Volume 34, Issue 2, Page 1290-1301, January 2020. Answering a question of Häggkvist and Scott, Verstraëte proved that every sufficiently large graph with average degree at least $k^2+19k+10$ contains $k$ vertex-disjoint cycles of consecutive even lengths. He further conjectured that the same holds for every graph $G$ with average degree at least $k^2+3k+2$. In

    更新日期:2020-06-30
  • Lattice Points in the Newton Polytopes of Key Polynomials
    SIAM J. Discret. Math. (IF 0.75) Pub Date : 2020-06-11
    Neil J. Y. Fan; Peter L. Guo; Simon C. Y. Peng; Sophie C. C. Sun

    SIAM Journal on Discrete Mathematics, Volume 34, Issue 2, Page 1281-1289, January 2020. We confirm a conjecture of Monical, Tokcan, and Yong on a characterization of the lattice points in the Newton polytopes of key polynomials.

    更新日期:2020-06-30
  • Levelness of Order Polytopes
    SIAM J. Discret. Math. (IF 0.75) Pub Date : 2020-06-08
    Christian Haase; Florian Kohl; Akiyoshi Tsuchiya

    SIAM Journal on Discrete Mathematics, Volume 34, Issue 2, Page 1261-1280, January 2020. Since Stanley's [Discrete Comput. Geom., 1 (1986), pp. 9--23] introduction of order polytopes, their geometry has been widely used to examine (algebraic) properties of finite posets. In this paper, we follow this route to examine the levelness property of order polytopes, a property generalizing Gorensteinness.

    更新日期:2020-06-30
  • Angle-Restricted Sets and Zero-Free Regions for the Permanent
    SIAM J. Discret. Math. (IF 0.75) Pub Date : 2020-06-04
    Pavel Etingof

    SIAM Journal on Discrete Mathematics, Volume 34, Issue 2, Page 1248-1260, January 2020. The goal of this paper is to give a systematic method of constructing zero-free regions for the permanent in the sense of Alexander Barvinok, i.e., regions in the complex plane such that the permanent of a square matrix of any size with entries from this region is nonzero. We do so by refining the approach of Barvinok

    更新日期:2020-06-30
  • On the Bias of Reed--Muller Codes over Odd Prime Fields
    SIAM J. Discret. Math. (IF 0.75) Pub Date : 2020-06-03
    Paul Beame; Shayan Oveis Gharan; Xin Yang

    SIAM Journal on Discrete Mathematics, Volume 34, Issue 2, Page 1232-1247, January 2020. We study the bias of random bounded-degree polynomials over odd prime fields and show that, with probability exponentially close to 1, $n$-variate polynomials of degree $d$ over $\mathbb{F}_p$ have bias at most $p^{-\Omega(n/d)}$. This also yields an exponential tail bound on the weight distribution of Reed--Muller

    更新日期:2020-06-30
  • Infinitesimal Rigidity in Normed Planes
    SIAM J. Discret. Math. (IF 0.75) Pub Date : 2020-05-26
    Sean Dewar

    SIAM Journal on Discrete Mathematics, Volume 34, Issue 2, Page 1205-1231, January 2020. We prove that a graph has an infinitesimally rigid placement in a non-Euclidean normed plane if and only if it contains a (2,2)-tight spanning subgraph. The method uses an inductive construction based on generalized Henneberg moves and the geometric properties of the normed plane. As a key step, rigid placements

    更新日期:2020-06-30
  • Minimum $T$-Joins and Signed-Circuit Covering
    SIAM J. Discret. Math. (IF 0.75) Pub Date : 2020-05-20
    Yezhou Wu; Dong Ye

    SIAM Journal on Discrete Mathematics, Volume 34, Issue 2, Page 1192-1204, January 2020. Let $G$ be a graph with edge set $E(G)$ and vertex set $V(G)$, and let $T$ be a vertex subset of $G$ with even cardinality. A $T$-join of $G$ is a subset $J$ of edges such that a vertex of $G$ is incident with an odd number of edges in $J$ if and only if the vertex belongs to $T$. Minimum $T$-joins have many applications

    更新日期:2020-06-30
  • Monomial Tropical Cones for Multicriteria Optimization
    SIAM J. Discret. Math. (IF 0.75) Pub Date : 2020-05-20
    Michael Joswig; Georg Loho

    SIAM Journal on Discrete Mathematics, Volume 34, Issue 2, Page 1172-1191, January 2020. We present an algorithm to compute all $n$ nondominated points of a multicriteria discrete optimization problem with $d$ objectives using at most $\mathcal{O}(n^{\lfloor d/2 \rfloor})$ scalarizations. The method is similar to algorithms by Przybylski, Gandibleux, and Ehrgott [Discrete Optim., 7 (2010), pp. 149--165]

    更新日期:2020-06-30
  • Set-Codes with Small Intersections and Small Discrepancies
    SIAM J. Discret. Math. (IF 0.75) Pub Date : 2020-05-18
    R. Gabrys; H. S. Dau; C. J. Colbourn; O. Milenkovic

    SIAM Journal on Discrete Mathematics, Volume 34, Issue 2, Page 1148-1171, January 2020. We address the new problem of designing large families of subsets of a common labeled ground set that simultaneously have small pairwise intersections and the property that the maximum discrepancy of the label values within each of the subsets is less than or equal to one. Our results include an upper bound on the

    更新日期:2020-06-30
  • Clique-Width for Graph Classes Closed under Complementation
    SIAM J. Discret. Math. (IF 0.75) Pub Date : 2020-05-05
    Alexandre Blanché; Konrad K. Dabrowski; Matthew Johnson; Vadim V. Lozin; Daniël Paulusma; Viktor Zamaraev

    SIAM Journal on Discrete Mathematics, Volume 34, Issue 2, Page 1107-1147, January 2020. Clique-width is an important graph parameter due to its algorithmic and structural properties. A graph class is hereditary if it can be characterized by a (not necessarily finite) set ${\cal H}$ of forbidden induced subgraphs. We study the boundedness of clique-width of hereditary graph classes closed under complementation

    更新日期:2020-06-30
  • Parameterized (Approximate) Defective Coloring
    SIAM J. Discret. Math. (IF 0.75) Pub Date : 2020-04-21
    Rémy Belmonte; Michael Lampis; Valia Mitsou

    SIAM Journal on Discrete Mathematics, Volume 34, Issue 2, Page 1084-1106, January 2020. In Defective Coloring we are given a graph $G=(V,E)$ and two integers ${\chi_d},\Delta^*$ and are asked if we can partition $V$ into ${\chi_d}$ color classes, so that each class induces a graph of maximum degree $\Delta^*$. We investigate the complexity of this generalization of Coloring with respect to several

    更新日期:2020-06-30
  • Upper Tails for Edge Eigenvalues of Random Graphs
    SIAM J. Discret. Math. (IF 0.75) Pub Date : 2020-04-14
    Bhaswar B. Bhattacharya; Shirshendu Ganguly

    SIAM Journal on Discrete Mathematics, Volume 34, Issue 2, Page 1069-1083, January 2020. The upper tail problem for the largest eigenvalue of the Erdös--Rényi random graph $\mathcal{G}_{n,p}$ is to estimate the probability that the largest eigenvalue of the adjacency matrix of $\mathcal{G}_{n,p}$ exceeds its typical value by a factor of $1+\delta$. In this note we show that for $\delta >0$ fixed, and

    更新日期:2020-04-14
  • Almost Envy-Freeness with General Valuations
    SIAM J. Discret. Math. (IF 0.75) Pub Date : 2020-04-08
    Benjamin Plaut; Tim Roughgarden

    SIAM Journal on Discrete Mathematics, Volume 34, Issue 2, Page 1039-1068, January 2020. The goal of fair division is to distribute resources among competing players in a “fair" way. Envy-freeness is the most extensively studied fairness notion in fair division. Envy-free allocations do not always exist with indivisible goods, motivating the study of relaxed versions of envy-freeness. We study the envy-freeness

    更新日期:2020-04-08
  • Finite Automata, Probabilistic Method, and Occurrence Enumeration of a Pattern in Words and Permutations
    SIAM J. Discret. Math. (IF 0.75) Pub Date : 2020-04-08
    Toufik Mansour; Reza Rastegar; Alexander Roitershtein

    SIAM Journal on Discrete Mathematics, Volume 34, Issue 2, Page 1011-1038, January 2020. The main theme of this paper is the enumeration of the order-isomorphic occurrence of a pattern in words and permutations. We mainly focus on asymptotic properties of the sequence $f_r^v(k,n),$ the number of $n$-array $k$-ary words that contain a given pattern $v$ exactly $r$ times. In addition, we study the asymptotic

    更新日期:2020-04-08
  • On a Ramsey--Turán Variant of the Hajnal--Szemerédi Theorem
    SIAM J. Discret. Math. (IF 0.75) Pub Date : 2020-04-02
    Rajko Nenadov; Yanitsa Pehova

    SIAM Journal on Discrete Mathematics, Volume 34, Issue 2, Page 1001-1010, January 2020. A seminal result of Hajnal and Szemerédi states that if a graph $G$ with $n$ vertices has minimum degree $\delta(G) \ge (r-1)n/r$ for some integer $r \ge 2$, then $G$ contains a $K_r$-factor, assuming $r$ divides $n$. Extremal examples which show optimality of the bound on $\delta(G)$ are very structured and, in

    更新日期:2020-04-02
  • Erratum for “On the Inequalities of Projected Volumes and the Constructible Region''
    SIAM J. Discret. Math. (IF 0.75) Pub Date : 2020-03-31
    Zihan Tan; Liwei Zeng

    SIAM Journal on Discrete Mathematics, Volume 34, Issue 1, Page 1000-1000, January 2020. This note is an erratum for the paper On the Inequalities of Projected Volumes and the Constructible Region [SIAM J. Discrete Math., 33 (2019), pp. 694--711]. There is a mistake in the proof of Theorem 4 in Section 3. However, Theorem 4 is itself correct (a proof can be found in [Inequalities on Projected Volumes

    更新日期:2020-03-31
  • Scattered Classes of Graphs
    SIAM J. Discret. Math. (IF 0.75) Pub Date : 2020-03-31
    O-joung Kwon; Sang-il Oum

    SIAM Journal on Discrete Mathematics, Volume 34, Issue 1, Page 972-999, January 2020. For a class $\mathcal C$ of graphs $G$ equipped with functions $f_G$ defined on subsets of $E(G)$ or $V(G)$, we say that $\mathcal{C}$ is $k$-$scattered$ with respect to $f_G$ if there exists a constant $\ell$ such that for every graph $G\in \mathcal C$, the domain of $f_G$ can be partitioned into subsets of size

    更新日期:2020-03-31
  • On the Profile of Multiplicities of Complete Subgraphs
    SIAM J. Discret. Math. (IF 0.75) Pub Date : 2020-03-31
    Uriel Feige; Anne Kenyon; Shimon Kogan

    SIAM Journal on Discrete Mathematics, Volume 34, Issue 1, Page 950-971, January 2020. Let $G$ be a 2-coloring of a complete graph on $n$ vertices, for sufficiently large $n$. We prove that $G$ contains at least $n^{(\frac{1}{4} - o(1))\log n}$ monochromatic complete subgraphs, thus improving over a lower bound of $n^{0.1576\log n}$ due to Székely [Combinatorica, 4 (1984), pp. 363--372]. We also present

    更新日期:2020-03-31
  • Large Deviation Theorem for Branches of the Random Binary Tree in the Horton--Strahler Analysis
    SIAM J. Discret. Math. (IF 0.75) Pub Date : 2020-03-30
    Ken Yamamoto

    SIAM Journal on Discrete Mathematics, Volume 34, Issue 1, Page 938-949, January 2020. The Horton--Strahler analysis is a graph-theoretic method to measure the bifurcation complexity of branching patterns, by defining a number called the order to each branch. The main result of this paper is a large deviation theorem for the number of branches of each order in a random binary tree. The rate function

    更新日期:2020-03-30
  • Efficient Error-Correcting Codes for Sliding Windows
    SIAM J. Discret. Math. (IF 0.75) Pub Date : 2020-03-24
    Ran Gelles; Rafail Ostrovsky; Alan Roytman

    SIAM Journal on Discrete Mathematics, Volume 34, Issue 1, Page 904-937, January 2020. We consider the task of communicating an (infinite) data stream in the sliding window model, where communication takes place over a noisy channel with an adversarial substitution noise rate up to 1. Specifically, for any noise level ${p<1}$ and any small $\varepsilon>0$, we design an efficient coding scheme, such

    更新日期:2020-03-24
  • Multitasking Capacity: Hardness Results and Improved Constructions
    SIAM J. Discret. Math. (IF 0.75) Pub Date : 2020-03-24
    Noga Alon; Jonathan D. Cohen; Thomas L Griffiths; Pasin Manurangsi; Daniel Reichman; Igor Shinkar; Tal Wagner; Alexander Yu

    SIAM Journal on Discrete Mathematics, Volume 34, Issue 1, Page 885-903, January 2020. We consider the problem of determining the maximal $\alpha \in (0,1]$ such that every matching $M$ of size $k$ (or at most $k$) in a bipartite graph $G$ contains an induced matching of size at least $\alpha |M|$. This measure was recently introduced in [N. Alon et al., Adv. Neural Inf. Process. Syst., 2017, pp. 2097--2106]

    更新日期:2020-03-24
  • An Improved Analysis of the Mömke--Svensson Algorithm for Graph-TSP on Subquartic Graphs
    SIAM J. Discret. Math. (IF 0.75) Pub Date : 2020-03-24
    Alantha Newman

    SIAM Journal on Discrete Mathematics, Volume 34, Issue 1, Page 865-884, January 2020. Mömke and Svensson presented a beautiful new approach for the traveling salesman problem on a graph metric (graph-TSP), which yields a 4/3-approximation guarantee on subcubic graphs as well as a substantial improvement over the 3/2-approximation guarantee of Christofides's algorithm on general graphs. The crux of

    更新日期:2020-03-24
  • Enumerating Vertices of Covering Polyhedra with Totally Unimodular Constraint Matrices
    SIAM J. Discret. Math. (IF 0.75) Pub Date : 2020-03-23
    Khaled Elbassioni; Kazuhisa Makino

    SIAM Journal on Discrete Mathematics, Volume 34, Issue 1, Page 843-864, January 2020. We give an incremental polynomial time algorithm for enumerating the vertices of any polyhedron $P=P(A,\b1)=\{x\in \mathbb{R}^n \mid Ax\geq \b1,~x\geq \b0\}$, when $A$ is a totally unimodular matrix. Our algorithm is based on decomposing the hypergraph transversal problem for unimodular hypergraphs using Seymour's

    更新日期:2020-03-23
  • Sparsification of Binary CSPs
    SIAM J. Discret. Math. (IF 0.75) Pub Date : 2020-03-23
    Silvia Butti; Stanislav Živný

    SIAM Journal on Discrete Mathematics, Volume 34, Issue 1, Page 825-842, January 2020. A cut $\varepsilon$-sparsifier of a weighted graph $G$ is a reweighted subgraph of $G$ of (quasi)linear size that preserves the size of all cuts up to a multiplicative factor of $\varepsilon$. Since their introduction by Benczúr and Karger [Approximating s-t minimum cuts in O͂($n^2$) time, in Proceedings of the Twenty-Eighth

    更新日期:2020-03-23
  • The Second-Moment Phenomenon for Monochromatic Subgraphs
    SIAM J. Discret. Math. (IF 0.75) Pub Date : 2020-03-23
    Bhaswar B. Bhattacharya; Somabha Mukherjee; Sumit Mukherjee

    SIAM Journal on Discrete Mathematics, Volume 34, Issue 1, Page 794-824, January 2020. What is the chance that among a group of $n$ friends, there are $s$ friends all of whom have the same birthday? This is the celebrated birthday problem which can be formulated as the existence of a monochromatic $s$-clique $K_s$ ($s$-matching birthdays) in the complete graph $K_n$, where every vertex of $K_n$ is uniformly

    更新日期:2020-03-23
  • Sampling in Uniqueness from the Potts and Random-Cluster Models on Random Regular Graphs
    SIAM J. Discret. Math. (IF 0.75) Pub Date : 2020-03-23
    Antonio Blanca; Andreas Galanis; Leslie Ann Goldberg; Daniel Štefankovič; Eric Vigoda; Kuan Yang

    SIAM Journal on Discrete Mathematics, Volume 34, Issue 1, Page 742-793, January 2020. We consider the problem of sampling from the Potts model on random regular graphs. It is conjectured that sampling is possible when the temperature of the model is in the so-called uniqueness regime of the regular tree, but positive algorithmic results have been for the most part elusive. In this paper, for all integers

    更新日期:2020-03-23
  • On Expressing Majority as a Majority of Majorities
    SIAM J. Discret. Math. (IF 0.75) Pub Date : 2020-03-17
    Christian Engels; Mohit Garg; Kazuhisa Makino; Anup Rao

    SIAM Journal on Discrete Mathematics, Volume 34, Issue 1, Page 730-741, January 2020. If $k

    更新日期:2020-03-17
  • Length of the Longest Common Subsequence between Overlapping Words
    SIAM J. Discret. Math. (IF 0.75) Pub Date : 2020-03-12
    Boris Bukh; Raymond Hogenson

    SIAM Journal on Discrete Mathematics, Volume 34, Issue 1, Page 721-729, January 2020. Given two random finite sequences from $[k]^n$ such that a prefix of the first sequence is a suffix of the second, we examine the length of their longest common subsequence (LCS). If $\ell$ is the length of the overlap, we prove that the expected length of an LCS is approximately $\max(\ell, {E}[L_n])$, where $L_n$

    更新日期:2020-03-12
  • L-Infinity Optimization to Bergman Fans of Matroids with an Application to Phylogenetics
    SIAM J. Discret. Math. (IF 0.75) Pub Date : 2020-03-12
    Daniel Irving Bernstein

    SIAM Journal on Discrete Mathematics, Volume 34, Issue 1, Page 701-720, January 2020. Given a dissimilarity map $\delta$ on a finite set $X$, the set of ultrametrics (equidistant tree metrics) which are $l^\infty$-nearest to $\delta$ is a tropical polytope. We give an internal description of this tropical polytope which we use to derive a polynomial-time checkable test for the condition that all ultrametrics

    更新日期:2020-03-12
  • The Impact of Locality in the Broadcast Congested Clique Model
    SIAM J. Discret. Math. (IF 0.75) Pub Date : 2020-03-12
    F. Becker; P. Montealegre; I. Rapaport; I. Todinca

    SIAM Journal on Discrete Mathematics, Volume 34, Issue 1, Page 682-700, January 2020. The broadcast congested clique model (BClique) is a message-passing model of distributed computation where $n$ nodes communicate with each other in synchronous rounds. First, in this paper we prove that there is a one-round, deterministic algorithm that reconstructs the input graph $G$ if the graph is $d$-degenerate

    更新日期:2020-03-12
  • Solving Partition Problems Almost Always Requires Pushing Many Vertices Around
    SIAM J. Discret. Math. (IF 0.75) Pub Date : 2020-03-10
    Iyad Kanj; Christian Komusiewicz; Manuel Sorge; Erik Jan van Leeuwen

    SIAM Journal on Discrete Mathematics, Volume 34, Issue 1, Page 640-681, January 2020. A fundamental graph problem is to recognize whether the vertex set of a graph $G$ can be bipartitioned into sets $A$ and $B$ such that $G[A]$ and $G[B]$ satisfy properties $\Pi_A$ and $\Pi_B$, respectively. This so-called $(\Pi_A,\Pi_B)$-Recognition problem generalizes, amongst others, the recognition of 3-colorable

    更新日期:2020-03-10
  • A Continuous Family of Marked Poset Polytopes
    SIAM J. Discret. Math. (IF 0.75) Pub Date : 2020-03-03
    Xin Fang; Ghislain Fourier; Jan-Philipp Litza; Christoph Pegel

    SIAM Journal on Discrete Mathematics, Volume 34, Issue 1, Page 611-639, January 2020. For any marked poset we define a continuous family of polytopes, parametrized by a hypercube, generalizing the notions of marked order and marked chain polytopes. By providing transfer maps, we show that the vertices of the hypercube parametrize an Ehrhart equivalent family of lattice polytopes. The combinatorial

    更新日期:2020-03-03
  • On the Minimum Degree Required for a Triangle Decomposition
    SIAM J. Discret. Math. (IF 0.75) Pub Date : 2020-03-03
    Peter J. Dukes; Daniel Horsley

    SIAM Journal on Discrete Mathematics, Volume 34, Issue 1, Page 597-610, January 2020. We prove that, for sufficiently large $n$, every graph of order $n$ with minimum degree at least $0.852n$ has a fractional edge-decomposition into triangles. We do this by refining a method used by Dross [SIAM J. Discrete Math., 30 (2016), pp. 36--42] to establish a bound of $0.9n$. By a result of Barber, Kühn, Lo

    更新日期:2020-03-03
  • A Dichotomy Theorem for First-Fit Chain Partitions
    SIAM J. Discret. Math. (IF 0.75) Pub Date : 2020-03-03
    Kevin G. Milans; Michael C. Wigal

    SIAM Journal on Discrete Mathematics, Volume 34, Issue 1, Page 586-596, January 2020. First-Fit is a greedy algorithm for partitioning the elements of a poset into chains. Let $\mathrm{FF}(w,Q)$ be the maximum number of chains that First-Fit uses on a $Q$-free poset of width $w$. A result due to Bosek, Krawczyk, and Matecki states that $\mathrm{FF}(w,Q)$ is finite when $Q$ has width at most $2$. We

    更新日期:2020-03-03
  • Finding Submodularity Hidden in Symmetric Difference
    SIAM J. Discret. Math. (IF 0.75) Pub Date : 2020-03-03
    Junpei Nakashima; Yukiko Yamauchi; Shuji Kijima; Masafumi Yamashita

    SIAM Journal on Discrete Mathematics, Volume 34, Issue 1, Page 571-585, January 2020. A set function $f$ on a finite set $V$ is submodular if $f(X) + f(Y) \geq f(X \cup Y) + f(X \cap Y)$ for any pair $X, Y \subseteq V$. The symmetric difference transformation (SD-transformation) of $f$ by a canonical set $S \subseteq V$ is a set function $g$ given by $g(X) = f(X \vartriangle S)$ for $X \subseteq V$

    更新日期:2020-03-03
  • Turán Numbers of Bipartite Subdivisions
    SIAM J. Discret. Math. (IF 0.75) Pub Date : 2020-03-03
    Tao Jiang; Yu Qiu

    SIAM Journal on Discrete Mathematics, Volume 34, Issue 1, Page 556-570, January 2020. Given a graph $H$, the Turán number $\mathrm{ex}(n,H)$ is the largest number of edges in an $H$-free graph on $n$ vertices. We make progress on a recent conjecture of Conlon, Janzer, and Lee [More on the Extremal Number of Subdivisions, arXiv:1903.10631v1, 2019] on the Turán numbers of bipartite graphs, which in turn

    更新日期:2020-03-03
  • Fractional Coloring of Planar Graphs of Girth Five
    SIAM J. Discret. Math. (IF 0.75) Pub Date : 2020-02-25
    Zdeněk Dvořák; Xiaolan Hu

    SIAM Journal on Discrete Mathematics, Volume 34, Issue 1, Page 538-555, January 2020. A graph $G$ is $(a:b)$-colorable if there exists an assignment of $b$-element subsets of $\{1,\ldots,a\}$ to vertices of $G$ such that sets assigned to adjacent vertices are disjoint. We first show that for every triangle-free planar graph $G$ and a vertex $x\in V(G)$, the graph $G$ has a set coloring $\varphi$ by

    更新日期:2020-02-25
  • Rainbow Coloring Hardness via Low Sensitivity Polymorphisms
    SIAM J. Discret. Math. (IF 0.75) Pub Date : 2020-02-25
    Venkatesan Guruswami; Sai Sandeep

    SIAM Journal on Discrete Mathematics, Volume 34, Issue 1, Page 520-537, January 2020. A $k$-uniform hypergraph is said to be $r$-rainbow colorable if there is an $r$-coloring of its vertices such that every hyperedge intersects all $r$ color classes. Given as input such a hypergraph, finding a $r$-rainbow coloring of it is NP-hard for all $k \ge 3$ and $r \ge 2$. Therefore, one settles for finding

    更新日期:2020-02-25
  • Circular Flows in Planar Graphs
    SIAM J. Discret. Math. (IF 0.75) Pub Date : 2020-02-19
    Daniel W. Cranston; Jiaao Li

    SIAM Journal on Discrete Mathematics, Volume 34, Issue 1, Page 497-519, January 2020. For integers $a\ge 2b>0$, a circular $a/b$-flow is a flow that takes values from $\{\pm b, \pm(b+1), \dots, \pm(a-b)\}$. The Planar Circular Flow Conjecture states that every $2k$-edge-connected planar graph admits a circular $(2+\frac{2}{k})$-flow. The cases $k=1$ and $k=2$ are equivalent to the Four Color Theorem

    更新日期:2020-02-19
  • A Notion of Total Dual Integrality for Convex, Semidefinite, and Extended Formulations
    SIAM J. Discret. Math. (IF 0.75) Pub Date : 2020-02-19
    Marcel K. de Carli Silva; Levent Tunçel

    SIAM Journal on Discrete Mathematics, Volume 34, Issue 1, Page 470-496, January 2020. Total dual integrality is a powerful and unifying concept in polyhedral combinatorics and integer programming that enables the refinement of geometric min-max relations given by linear programming strong duality into combinatorial min-max theorems. The definition of a linear inequality system being totally dual integral

    更新日期:2020-02-19
  • Obstructions for Three-Coloring and List Three-Coloring $H$-Free Graphs
    SIAM J. Discret. Math. (IF 0.75) Pub Date : 2020-02-19
    Maria Chudnovsky; Jan Goedgebeur; Oliver Schaudt; Mingxian Zhong

    SIAM Journal on Discrete Mathematics, Volume 34, Issue 1, Page 431-469, January 2020. A graph is $H$-free if it has no induced subgraph isomorphic to $H$. We characterize all graphs $H$ for which there are only finitely many minimal non-3-colorable $H$-free graphs. Such a characterization was previously known only in the case when $H$ is connected. This solves a problem posed by Golovach et al. As

    更新日期:2020-02-19
  • Directed Path-Decompositions
    SIAM J. Discret. Math. (IF 0.75) Pub Date : 2020-02-12
    Joshua Erde

    SIAM Journal on Discrete Mathematics, Volume 34, Issue 1, Page 415-430, January 2020. Many of the tools developed for the theory of tree-decompositions of graphs do not work for directed graphs. In this paper we show that some of the most basic tools do work in the case where the model digraph is a directed path. Using these tools we define a notion of a directed blockage in a digraph and prove a min-max

    更新日期:2020-02-12
  • Weighted Games of Best Choice
    SIAM J. Discret. Math. (IF 0.75) Pub Date : 2020-02-12
    Brant Jones

    SIAM Journal on Discrete Mathematics, Volume 34, Issue 1, Page 399-414, January 2020. The game of best choice (also known as the secretary problem) is a model for sequential decision making with a long history and many variations. The classical setup assumes that the sequence of candidate rankings is uniformly distributed. Given a statistic on the symmetric group, one can instead weight each permutation

    更新日期:2020-02-12
  • Books versus Triangles at the Extremal Density
    SIAM J. Discret. Math. (IF 0.75) Pub Date : 2020-02-12
    David Conlon; Jacob Fox; Benny Sudakov

    SIAM Journal on Discrete Mathematics, Volume 34, Issue 1, Page 385-398, January 2020. A celebrated result of Mantel shows that every graph on n vertices with $\lfloor n^2/4 \rfloor + 1$ edges must contain a triangle. A robust version of this result, due to Rademacher, says that there must, in fact, be at least $\lfloor n/2 \rfloor$ triangles in any such graph. Another strengthening, due to the combined

    更新日期:2020-02-12
  • Combinatorics for General Kinetically Constrained Spin Models
    SIAM J. Discret. Math. (IF 0.75) Pub Date : 2020-02-12
    Laure Marêché

    SIAM Journal on Discrete Mathematics, Volume 34, Issue 1, Page 370-384, January 2020. We study the set of possible configurations for a general kinetically constrained model (KCM), a nonmonotone version of the $\mathcal{U}$-bootstrap percolation cellular automata. We solve a combinatorial question that is a generalization of a problem addressed by Chung, Diaconis, and Graham [Adv. in Appl. Math., 27

    更新日期:2020-02-12
  • Ramsey Problems for Berge Hypergraphs
    SIAM J. Discret. Math. (IF 0.75) Pub Date : 2020-02-12
    Dániel Gerbner; Abhishek Methuku; Gholamreza Omidi; Máté Vizer

    SIAM Journal on Discrete Mathematics, Volume 34, Issue 1, Page 351-369, January 2020. For a graph G, a hypergraph $\mathcal{H}$ is a Berge copy of G (or a Berge-G in short) if there is a bijection $f : E(G) \rightarrow E(\mathcal{H})$ such that for each $e \in E(G)$ we have $e \subseteq f(e)$. We denote the family of r-uniform hypergraphs that are Berge copies of G by $B^rG$. For families of r-uniform

    更新日期:2020-02-12
  • Homomorphism Reconfiguration via Homotopy
    SIAM J. Discret. Math. (IF 0.75) Pub Date : 2020-01-30
    Marcin Wrochna

    SIAM Journal on Discrete Mathematics, Volume 34, Issue 1, Page 328-350, January 2020. For a fixed graph H, we consider the H-Recoloring problem: given a graph G and two H-colorings of G, i.e., homomorphisms from G to H, can one be transformed into the other by changing one color at a time, maintaining an H-coloring throughout. This is the same as finding a path in the Hom(G,H) complex. For H=K_k this

    更新日期:2020-01-30
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