SIAM Journal on Discrete Mathematics最新文献_第6页

Spanning Bipartite Quadrangulations of Triangulations of the Projective Plane 投影平面三角剖分的跨二元四分法

IF 0.8 3区数学

SIAM Journal on Discrete Mathematics Pub Date : 2024-04-08 DOI: 10.1137/23m1566960

Kenta Noguchi

引用次数: 0

The Rainbow Saturation Number Is Linear 彩虹饱和度数值是线性的

IF 0.8 3区数学

SIAM Journal on Discrete Mathematics Pub Date : 2024-04-08 DOI: 10.1137/23m1566881

Natalie Behague, Tom Johnston, Shoham Letzter, Natasha Morrison, Shannon Ogden

引用次数: 0

On the Gap Between Hereditary Discrepancy and the Determinant Lower Bound 论遗传差异与决定因素下限之间的差距

IF 0.8 3区数学

SIAM Journal on Discrete Mathematics Pub Date : 2024-04-05 DOI: 10.1137/23m1566790

Lily Li, Aleksandar Nikolov

{"title":"On the Gap Between Hereditary Discrepancy and the Determinant Lower Bound","authors":"Lily Li, Aleksandar Nikolov","doi":"10.1137/23m1566790","DOIUrl":"https://doi.org/10.1137/23m1566790","url":null,"abstract":"SIAM Journal on Discrete Mathematics, Volume 38, Issue 2, Page 1222-1238, June 2024. Abstract. The determinant lower bound of Lovász, Spencer, and Vesztergombi [European J. Combin., 7 (1986), pp. 151–160] is a general way to prove lower bounds on the hereditary discrepancy of a set system. In their paper, Lovász, Spencer, and Vesztergombi asked if hereditary discrepancy can also be bounded from above by a function of the determinant lower bound. This was answered in the negative by Hoffman, and the largest known multiplicative gap between the two quantities for a set system of [math] subsets of a universe of size [math] is on the order of [math]. On the other hand, building upon work of Matoušek [Proc. Amer. Math. Soc., 141 (2013), pp. 451–460], Jiang and Reis [in Proceedings of the Symposium on Simplicity in Algorithms (SOSA), SIAM, Philadelphia, 2022, pp. 308–313] showed that this gap is always bounded up to constants by [math]. This is tight when [math] is polynomial in [math] but leaves open the case of large [math]. We show that the bound of Jiang and Reis is tight for nearly the entire range of [math]. Our proof amplifies the discrepancy lower bounds of a set system derived from the discrete Haar basis via Kronecker products.","PeriodicalId":49530,"journal":{"name":"SIAM Journal on Discrete Mathematics","volume":"242 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140563420","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

Maximum Matchings and Popularity 最大匹配度和人气

IF 0.8 3区数学

SIAM Journal on Discrete Mathematics Pub Date : 2024-04-04 DOI: 10.1137/22m1523248

Telikepalli Kavitha

{"title":"Maximum Matchings and Popularity","authors":"Telikepalli Kavitha","doi":"10.1137/22m1523248","DOIUrl":"https://doi.org/10.1137/22m1523248","url":null,"abstract":"SIAM Journal on Discrete Mathematics, Volume 38, Issue 2, Page 1202-1221, June 2024. Abstract. Let [math] be a bipartite graph where every node has a strict ranking of its neighbors. For any node, its preferences over neighbors extend naturally to preferences over matchings. A maximum matching [math] in [math] is a popular max-matching if there is no maximum matching more popular than [math]. In other words, for any maximum matching [math], the number of nodes that prefer [math] to [math] is at least the number of nodes that prefer [math] to [math]. It is known that popular max-matchings always exist in [math] and one such matching can be efficiently computed. In this paper we are in the weighted setting, i.e., there is a cost function [math], and our goal is to find a min-cost popular max-matching. We prove that such a matching can be computed in polynomial time by showing a compact extended formulation for the popular max-matching polytope. By contrast, it is known that the popular matching polytope has near-exponential extension complexity and finding a min-cost popular matching is NP-hard. We also consider Pareto-optimality. Though it is easy to find a Pareto-optimal matching/max-matching, we show that it is NP-hard to find a min-cost Pareto-optimal matching/max-matching.","PeriodicalId":49530,"journal":{"name":"SIAM Journal on Discrete Mathematics","volume":"39 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140563145","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

Circuit Decompositions of Binary Matroids 二元矩阵的电路分解

IF 0.8 3区数学

SIAM Journal on Discrete Mathematics Pub Date : 2024-04-01 DOI: 10.1137/23m1587439

Bryce Frederickson, Lukas Michel

引用次数: 0

Erratum: More Applications of the [math]-Neighbor Equivalence: Acyclicity and Connectivity Constraints 勘误：[math]-Neighbor Equivalence 的更多应用：循环性和连接性约束

IF 0.8 3区数学

SIAM Journal on Discrete Mathematics Pub Date : 2024-03-25 DOI: 10.1137/23m157644x

Benjamin Bergougnoux, Mamadou M. Kanté

引用次数: 0

List-3-Coloring Ordered Graphs with a Forbidden Induced Subgraphs 列表-3-使用禁止诱导子图为有序图着色

IF 0.8 3区数学

SIAM Journal on Discrete Mathematics Pub Date : 2024-03-20 DOI: 10.1137/22m1515768

Sepehr Hajebi, Yanjia Li, Sophie Spirkl

{"title":"List-3-Coloring Ordered Graphs with a Forbidden Induced Subgraphs","authors":"Sepehr Hajebi, Yanjia Li, Sophie Spirkl","doi":"10.1137/22m1515768","DOIUrl":"https://doi.org/10.1137/22m1515768","url":null,"abstract":"SIAM Journal on Discrete Mathematics, Volume 38, Issue 1, Page 1158-1190, March 2024. Abstract. The List-3-Coloring Problem is to decide, given a graph [math] and a list [math] of colors assigned to each vertex [math] of [math], whether [math] admits a proper coloring [math] with [math] for every vertex [math] of [math], and the 3-Coloring Problem is the List-3-Coloring Problem on instances with [math] for every vertex [math] of [math]. The List-3-Coloring Problem is a classical NP-complete problem, and it is well-known that while restricted to [math]-free graphs (meaning graphs with no induced subgraph isomorphic to a fixed graph [math]), it remains NP-complete unless [math] is isomorphic to an induced subgraph of a path. However, the current state of art is far from proving this to be sufficient for a polynomial time algorithm; in fact, the complexity of the 3-Coloring Problem on [math]-free graphs (where [math] denotes the eight-vertex path) is unknown. Here we consider a variant of the List-3-Coloring Problem called the Ordered Graph List-3-Coloring Problem, where the input is an ordered graph, that is, a graph along with a linear order on its vertex set. For ordered graphs [math] and [math], we say [math] is [math]-free if [math] is not isomorphic to an induced subgraph of [math] with the isomorphism preserving the linear order. We prove, assuming [math] to be an ordered graph, a nearly complete dichotomy for the Ordered Graph List-3-Coloring Problem restricted to [math]-free ordered graphs. In particular, we show that the problem can be solved in polynomial time if [math] has at most one edge, and remains NP-complete if [math] has at least three edges. Moreover, in the case where [math] has exactly two edges, we give a complete dichotomy when the two edges of [math] share an end, and prove several NP-completeness results when the two edges of [math] do not share an end, narrowing the open cases down to three very special types of two-edge ordered graphs.","PeriodicalId":49530,"journal":{"name":"SIAM Journal on Discrete Mathematics","volume":"1 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140205504","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

Transportation Distance between Probability Measures on the Infinite Regular Tree 无限规则树上概率量之间的传输距离

IF 0.8 3区数学

SIAM Journal on Discrete Mathematics Pub Date : 2024-03-15 DOI: 10.1137/21m1448781

Pakawut Jiradilok, Supanat Kamtue

引用次数: 0

Rainbow Saturation for Complete Graphs 完整图形的彩虹饱和度

IF 0.8 3区数学

SIAM Journal on Discrete Mathematics Pub Date : 2024-03-14 DOI: 10.1137/23m1565875

Debsoumya Chakraborti, Kevin Hendrey, Ben Lund, Casey Tompkins

{"title":"Rainbow Saturation for Complete Graphs","authors":"Debsoumya Chakraborti, Kevin Hendrey, Ben Lund, Casey Tompkins","doi":"10.1137/23m1565875","DOIUrl":"https://doi.org/10.1137/23m1565875","url":null,"abstract":"SIAM Journal on Discrete Mathematics, Volume 38, Issue 1, Page 1090-1112, March 2024. Abstract. We call an edge-colored graph rainbow if all of its edges receive distinct colors. An edge-colored graph [math] is called [math]-rainbow saturated if [math] does not contain a rainbow copy of [math] and adding an edge of any color to [math] creates a rainbow copy of [math]. The rainbow saturation number [math] is the minimum number of edges in an [math]-vertex [math]-rainbow saturated graph. Girão, Lewis, and Popielarz conjectured that [math] for fixed [math]. Disproving this conjecture, we establish that for every [math], there exists a constant [math] such that [math] and [math]. Recently, Behague, Johnston, Letzter, Morrison, and Ogden independently gave a slightly weaker upper bound which was sufficient to disprove the conjecture. They also introduced the weak rainbow saturation number and asked whether this is equal to the rainbow saturation number of [math], since the standard weak saturation number of complete graphs equals the standard saturation number. Surprisingly, our lower bound separates the rainbow saturation number from the weak rainbow saturation number, answering this question in the negative. The existence of the constant [math] resolves another of their questions in the affirmative for complete graphs. Furthermore, we show that the conjecture of Girão, Lewis, and Popielarz is true if we have an additional assumption that the edge-colored [math]-rainbow saturated graph must be rainbow. As an ingredient of the proof, we study graphs which are [math]-saturated with respect to the operation of deleting one edge and adding two edges.","PeriodicalId":49530,"journal":{"name":"SIAM Journal on Discrete Mathematics","volume":"29 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140151873","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

Shallow Minors, Graph Products, and Beyond-Planar Graphs 浅小数、图形积和超平面图形

IF 0.8 3区数学

SIAM Journal on Discrete Mathematics Pub Date : 2024-03-13 DOI: 10.1137/22m1540296

Robert Hickingbotham, David R. Wood

{"title":"Shallow Minors, Graph Products, and Beyond-Planar Graphs","authors":"Robert Hickingbotham, David R. Wood","doi":"10.1137/22m1540296","DOIUrl":"https://doi.org/10.1137/22m1540296","url":null,"abstract":"SIAM Journal on Discrete Mathematics, Volume 38, Issue 1, Page 1057-1089, March 2024. Abstract. The planar graph product structure theorem of Dujmović et al. [J. ACM, 67 (2020), 22] states that every planar graph is a subgraph of the strong product of a graph with bounded treewidth and a path. This result has been the key tool to resolve important open problems regarding queue layouts, nonrepetitive colorings, centered colorings, and adjacency labeling schemes. In this paper, we extend this line of research by utilizing shallow minors to prove analogous product structure theorems for several beyond-planar graph classes. The key observation that drives our work is that many beyond-planar graphs can be described as a shallow minor of the strong product of a planar graph with a small complete graph. In particular, we show that powers of bounded degree planar graphs, [math]-planar, [math]-cluster planar, fan-planar, and [math]-fan-bundle planar graphs have such a shallow-minor structure. Using a combination of old and new results, we deduce that these classes have bounded queue-number, bounded nonrepetitive chromatic number, polynomial [math]-centered chromatic numbers, linear strong coloring numbers, and cubic weak coloring numbers. In addition, we show that [math]-gap planar graphs have at least exponential local treewidth and, as a consequence, cannot be described as a subgraph of the strong product of a graph with bounded treewidth and a path.","PeriodicalId":49530,"journal":{"name":"SIAM Journal on Discrete Mathematics","volume":"16 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140125187","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