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Off-Diagonal Commonality of Graphs via Entropy 通过熵实现图形的非对角共性
IF 0.8 3区 数学
SIAM Journal on Discrete Mathematics Pub Date : 2024-08-27 DOI: 10.1137/23m1625342
Natalie Behague, Natasha Morrison, Jonathan A. Noel
{"title":"Off-Diagonal Commonality of Graphs via Entropy","authors":"Natalie Behague, Natasha Morrison, Jonathan A. Noel","doi":"10.1137/23m1625342","DOIUrl":"https://doi.org/10.1137/23m1625342","url":null,"abstract":"SIAM Journal on Discrete Mathematics, Volume 38, Issue 3, Page 2335-2360, September 2024. <br/> Abstract. A graph [math] is common if the limit as [math] of the minimum density of monochromatic labeled copies of [math] in an edge coloring of [math] with red and blue is attained by a sequence of quasirandom colorings. We apply an information-theoretic approach to show that certain graphs obtained from odd cycles and paths via gluing operations are common. In fact, for every pair [math] of such graphs, there exists [math] such that an appropriate linear combination of red copies of [math] and blue copies of [math] is minimized by a quasirandom coloring in which [math] edges are red; such a pair [math] is said to be [math]-common. Our approach exploits a strengthening of the common graph property for odd cycles that was recently proved using Schur convexity. We also exhibit a [math]-common pair [math] such that [math] is uncommon.","PeriodicalId":49530,"journal":{"name":"SIAM Journal on Discrete Mathematics","volume":"43 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142202431","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On Multicolor Turán Numbers 关于多色图兰数字
IF 0.8 3区 数学
SIAM Journal on Discrete Mathematics Pub Date : 2024-08-26 DOI: 10.1137/24m1639488
József Balogh, Anita Liebenau, Letícia Mattos, Natasha Morrison
{"title":"On Multicolor Turán Numbers","authors":"József Balogh, Anita Liebenau, Letícia Mattos, Natasha Morrison","doi":"10.1137/24m1639488","DOIUrl":"https://doi.org/10.1137/24m1639488","url":null,"abstract":"SIAM Journal on Discrete Mathematics, Volume 38, Issue 3, Page 2297-2311, September 2024. <br/> Abstract. We address a problem which is a generalization of Turán-type problems recently introduced by Imolay, Karl, Nagy, and Váli. Let [math] be a fixed graph and let [math] be the union of [math] edge-disjoint copies of [math], namely [math], where each [math] is isomorphic to a fixed graph [math] and [math] for all [math]. We call a subgraph [math] multicolored if [math] and [math] share at most one edge for all [math]. Define [math] to be the maximum value [math] such that there exists [math] on [math] vertices without a multicolored copy of [math]. We show that [math] and that all extremal graphs are close to a blow-up of the 5-cycle. This bound is tight up to the linear error term.","PeriodicalId":49530,"journal":{"name":"SIAM Journal on Discrete Mathematics","volume":"8 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142202433","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A Linear Bound for the Colin de Verdière Parameter [math] for Graphs Embedded on Surfaces 嵌入曲面的图形的科林-德-威尔第埃参数[数学]的线性约束
IF 0.8 3区 数学
SIAM Journal on Discrete Mathematics Pub Date : 2024-08-12 DOI: 10.1137/23m1623628
Camille Lanuel, Francis Lazarus, Rudi Pendavingh
{"title":"A Linear Bound for the Colin de Verdière Parameter [math] for Graphs Embedded on Surfaces","authors":"Camille Lanuel, Francis Lazarus, Rudi Pendavingh","doi":"10.1137/23m1623628","DOIUrl":"https://doi.org/10.1137/23m1623628","url":null,"abstract":"SIAM Journal on Discrete Mathematics, Volume 38, Issue 3, Page 2289-2296, September 2024. <br/> Abstract. We provide a combinatorial and self-contained proof of a result following from G. Besson [Ann. Inst. Fourier, 30 (1980), pp. 109–128] and Y. Colin de Verdière [Ann. Sci. Éc. Norm. Supér., 20 (1987), pp. 599–615] that for all graphs [math] embedded on a surface [math], the Colin de Verdière parameter [math] is upper bounded by [math].","PeriodicalId":49530,"journal":{"name":"SIAM Journal on Discrete Mathematics","volume":"46 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142202435","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Generalized Tuza’s Conjecture for Random Hypergraphs 随机超图的广义图扎猜想
IF 0.8 3区 数学
SIAM Journal on Discrete Mathematics Pub Date : 2024-07-30 DOI: 10.1137/23m1587014
Abdul Basit, David Galvin
{"title":"Generalized Tuza’s Conjecture for Random Hypergraphs","authors":"Abdul Basit, David Galvin","doi":"10.1137/23m1587014","DOIUrl":"https://doi.org/10.1137/23m1587014","url":null,"abstract":"SIAM Journal on Discrete Mathematics, Volume 38, Issue 3, Page 2260-2288, September 2024. <br/> Abstract. A celebrated conjecture of Tuza states that in any finite graph the minimum size of a cover of triangles by edges is at most twice the maximum size of a set of edge-disjoint triangles. For an [math]-uniform hypergraph ([math]-graph) [math], let [math] be the minimum size of a cover of edges by [math]-sets of vertices, and let [math] be the maximum size of a set of edges pairwise intersecting in fewer than [math] vertices. Aharoni and Zerbib proposed the following generalization of Tuza’s conjecture: For any [math]-graph [math], [math]. Let [math] be the uniformly random [math]-graph on [math] vertices. We show that for [math] and any [math], [math] satisfies the Aharoni–Zerbib conjecture with high probability (w.h.p.), i.e., with probability approaching 1 as [math]. We also show that there is a [math] such that for any [math] and any [math], [math] w.h.p. Furthermore, we may take [math], for any [math], by restricting to sufficiently large [math] (depending on [math]).","PeriodicalId":49530,"journal":{"name":"SIAM Journal on Discrete Mathematics","volume":"23 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141864261","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Phase Transitions for the Minimizers of the [math]-Frame Potentials in [math] [数学]中[数学]框架势最小值的相变
IF 0.8 3区 数学
SIAM Journal on Discrete Mathematics Pub Date : 2024-07-26 DOI: 10.1137/22m1539915
Radel Ben-Av, Xuemei Chen, Assaf Goldberger, Shujie Kang, Kasso A. Okoudjou
{"title":"Phase Transitions for the Minimizers of the [math]-Frame Potentials in [math]","authors":"Radel Ben-Av, Xuemei Chen, Assaf Goldberger, Shujie Kang, Kasso A. Okoudjou","doi":"10.1137/22m1539915","DOIUrl":"https://doi.org/10.1137/22m1539915","url":null,"abstract":"SIAM Journal on Discrete Mathematics, Volume 38, Issue 3, Page 2243-2259, September 2024. <br/> Abstract. Given [math] points [math] on the unit circle in [math] and a number [math], we investigate the minimizers of the functional [math]. While it is known that each of these minimizers is a spanning set for [math], less is known about their number as a function of [math] and [math] especially for relatively small [math]. In this paper we show that there is unique minimum for this functional for all [math] and all odd [math]. In addition, we present some numerical results suggesting the emergence of a phase transition phenomenon for these minimizers. More specifically, for [math] odd, there exists a sequence of points [math] so that a unique (up to some isometries) minimizer exists on each of the subintervals [math].","PeriodicalId":49530,"journal":{"name":"SIAM Journal on Discrete Mathematics","volume":"16 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141771395","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Solving the Maximum Popular Matching Problem with Matroid Constraints 利用矩阵约束解决最大热门匹配问题
IF 0.8 3区 数学
SIAM Journal on Discrete Mathematics Pub Date : 2024-07-24 DOI: 10.1137/23m1579911
Gergely Csáji, Tamás Király, Yu Yokoi
{"title":"Solving the Maximum Popular Matching Problem with Matroid Constraints","authors":"Gergely Csáji, Tamás Király, Yu Yokoi","doi":"10.1137/23m1579911","DOIUrl":"https://doi.org/10.1137/23m1579911","url":null,"abstract":"SIAM Journal on Discrete Mathematics, Volume 38, Issue 3, Page 2226-2242, September 2024. <br/> Abstract. We consider the problem of finding a maximum popular matching in a many-to-many matching setting with two-sided preferences and matroid constraints. This problem was proposed by Kamiyama [Theoret. Comput. Sci., 809 (2020), pp. 265–276] and solved in the special case where matroids are base orderable. Utilizing a newly shown matroid exchange property, we show that the problem is tractable for arbitrary matroids. We further investigate a different notion of popularity, where the agents vote with respect to lexicographic preferences, and show that both existence and verification problems become coNP-hard even in the [math]-matching case.","PeriodicalId":49530,"journal":{"name":"SIAM Journal on Discrete Mathematics","volume":"28 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141771396","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
M-Convexity of Vexillary Grothendieck Polynomials via Bubbling 通过气泡实现格罗内迪克多项式的 M-凸性
IF 0.8 3区 数学
SIAM Journal on Discrete Mathematics Pub Date : 2024-07-23 DOI: 10.1137/23m1599082
Elena S. Hafner, Karola Mészáros, Linus Setiabrata, Avery St. Dizier
{"title":"M-Convexity of Vexillary Grothendieck Polynomials via Bubbling","authors":"Elena S. Hafner, Karola Mészáros, Linus Setiabrata, Avery St. Dizier","doi":"10.1137/23m1599082","DOIUrl":"https://doi.org/10.1137/23m1599082","url":null,"abstract":"SIAM Journal on Discrete Mathematics, Volume 38, Issue 3, Page 2194-2225, September 2024. <br/> Abstract. We introduce bubbling diagrams and show that they compute the support of the Grothendieck polynomial of any vexillary permutation. Using these diagrams, we show that the support of the top homogeneous component of such a Grothendieck polynomial coincides with the support of the dual character of an explicit flagged Weyl module. We also show that the homogenized Grothendieck polynomial of a vexillary permutation has M-convex support.","PeriodicalId":49530,"journal":{"name":"SIAM Journal on Discrete Mathematics","volume":"34 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141771397","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Optimal Adjacency Labels for Subgraphs of Cartesian Products 笛卡尔积子图的最佳邻接标签
IF 0.8 3区 数学
SIAM Journal on Discrete Mathematics Pub Date : 2024-07-22 DOI: 10.1137/23m1587713
Louis Esperet, Nathaniel Harms, Viktor Zamaraev
{"title":"Optimal Adjacency Labels for Subgraphs of Cartesian Products","authors":"Louis Esperet, Nathaniel Harms, Viktor Zamaraev","doi":"10.1137/23m1587713","DOIUrl":"https://doi.org/10.1137/23m1587713","url":null,"abstract":"SIAM Journal on Discrete Mathematics, Volume 38, Issue 3, Page 2181-2193, September 2024. <br/> Abstract. For any hereditary graph class [math], we construct optimal adjacency labeling schemes for the classes of subgraphs and induced subgraphs of Cartesian products of graphs in [math]. As a consequence, we show that if [math] admits efficient adjacency labels (or, equivalently, small induced-universal graphs) meeting the information-theoretic minimum, then so do the classes of subgraphs and induced subgraphs of Cartesian products of graphs in [math]. Our proof uses ideas from randomized communication complexity, hashing, and additive combinatorics and improves upon recent results of Chepoi, Labourel, and Ratel [J. Graph Theory, 93 (2020), pp. 64–87].","PeriodicalId":49530,"journal":{"name":"SIAM Journal on Discrete Mathematics","volume":"161 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141745427","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Graphs with Large Girth and Chromatic Number are Hard for Nullstellensatz 具有较大周长和色度数的图形难以实现零点定理
IF 0.8 3区 数学
SIAM Journal on Discrete Mathematics Pub Date : 2024-07-11 DOI: 10.1137/23m1553273
Julian Romero, Levent Tunçel
{"title":"Graphs with Large Girth and Chromatic Number are Hard for Nullstellensatz","authors":"Julian Romero, Levent Tunçel","doi":"10.1137/23m1553273","DOIUrl":"https://doi.org/10.1137/23m1553273","url":null,"abstract":"SIAM Journal on Discrete Mathematics, Volume 38, Issue 3, Page 2108-2131, September 2024. <br/> Abstract. We study the computational efficiency of approaches, based on Hilbert’s Nullstellensatz, which use systems of linear equations for detecting noncolorability of graphs having large girth and chromatic number. We show that for every non-[math]-colorable graph with [math] vertices and girth [math], the algorithm is required to solve systems of size at least [math] in order to detect its non-[math]-colorability.","PeriodicalId":49530,"journal":{"name":"SIAM Journal on Discrete Mathematics","volume":"27 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141609410","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Product Structure Extension of the Alon–Seymour–Thomas Theorem 阿伦-塞缪尔-托马斯定理的乘积结构扩展
IF 0.8 3区 数学
SIAM Journal on Discrete Mathematics Pub Date : 2024-07-09 DOI: 10.1137/23m1591773
Marc Distel, Vida Dujmović, David Eppstein, Robert Hickingbotham, Gwenaël Joret, Piotr Micek, Pat Morin, Michał T. Seweryn, David R. Wood
{"title":"Product Structure Extension of the Alon–Seymour–Thomas Theorem","authors":"Marc Distel, Vida Dujmović, David Eppstein, Robert Hickingbotham, Gwenaël Joret, Piotr Micek, Pat Morin, Michał T. Seweryn, David R. Wood","doi":"10.1137/23m1591773","DOIUrl":"https://doi.org/10.1137/23m1591773","url":null,"abstract":"SIAM Journal on Discrete Mathematics, Volume 38, Issue 3, Page 2095-2107, September 2024. <br/> Abstract. Alon, Seymour, and Thomas [J. Amer. Math. Soc., 3 (1990), pp. 801–808] proved that every [math]-vertex graph excluding [math] as a minor has treewidth less than [math]. Illingworth, Scott, and Wood [Product Structure of Graphs with an Excluded Minor, preprint, arXiv:2104.06627, 2022] recently refined this result by showing that every such graph is a subgraph of some graph with treewidth [math], where each vertex is blown up by a complete graph of order [math]. Solving an open problem of Illingworth, Scott, and Wood [2022], we prove that the treewidth bound can be reduced to 4 while keeping blowups of order [math]. As an extension of the Lipton–Tarjan theorem, in the case of planar graphs, we show that the treewidth can be further reduced to 2, which is best possible. We generalize this result for [math]-minor-free graphs, with blowups of order [math]. This setting includes graphs embeddable on any fixed surface.","PeriodicalId":49530,"journal":{"name":"SIAM Journal on Discrete Mathematics","volume":"39 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141567200","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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