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  • 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
  • Upper Tail Bounds for Cycles
    SIAM J. Discret. Math. (IF 0.75) Pub Date : 2020-07-20
    Abigail Raz

    SIAM Journal on Discrete Mathematics, Volume 34, Issue 3, Page 1559-1586, January 2020. This paper examines bounds on upper tails for cycle counts in $G_{n,p}$. For a fixed graph $H$ define $\xi_H= \xi_H^{n,p}$ to be the number of copies of $H$ in $G_{n,p}$. It is a much studied and surprisingly difficult problem to understand the upper tail of the distribution of $\xi_H$, for example, to estimate

    更新日期:2020-07-20
  • Finer Tight Bounds for Coloring on Clique-Width
    SIAM J. Discret. Math. (IF 0.75) Pub Date : 2020-07-13
    Michael Lampis

    SIAM Journal on Discrete Mathematics, Volume 34, Issue 3, Page 1538-1558, January 2020. We revisit the complexity of the classical $k$-Coloring problem parameterized by clique-width. This is a very well-studied problem that becomes highly intractable when the number of colors $k$ is large. However, much less is known on its complexity for small, concrete values of $k$. In this paper, we completely

    更新日期:2020-07-14
  • The Unbreakable Frame Matroids
    SIAM J. Discret. Math. (IF 0.75) Pub Date : 2020-07-08
    Tara Fife; Dillon Mayhew; James Oxley; Charles Semple

    SIAM Journal on Discrete Mathematics, Volume 34, Issue 3, Page 1522-1537, January 2020. A connected matroid $M$ is unbreakable if, for each of its flats $F$, the matroid $M/F$ is connected or, equivalently, if $M^*$ has no two skew circuits. Pfeil showed that a simple graphic matroid $M(G)$ is unbreakable exactly when $G$ is either a cycle or a complete graph. We extend this result to describe which

    更新日期:2020-07-14
  • 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
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