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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
{"title":"Erratum: More Applications of the [math]-Neighbor Equivalence: Acyclicity and Connectivity Constraints","authors":"Benjamin Bergougnoux, Mamadou M. Kanté","doi":"10.1137/23m157644x","DOIUrl":"https://doi.org/10.1137/23m157644x","url":null,"abstract":"SIAM Journal on Discrete Mathematics, Volume 38, Issue 1, Page 1191-1192, March 2024. <br/> Abstract. We spotted an error in our publication More applications of the d-neighbor equivalence: Acyclicity and Connetivity constraints [SIAM J. Discrete Math., 35 (2021), pp. 1881–1926]. We explain the problem and suggest a simple correction.","PeriodicalId":49530,"journal":{"name":"SIAM Journal on Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140299019","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
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. <br/> 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":null,"pages":null},"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
{"title":"Transportation Distance between Probability Measures on the Infinite Regular Tree","authors":"Pakawut Jiradilok, Supanat Kamtue","doi":"10.1137/21m1448781","DOIUrl":"https://doi.org/10.1137/21m1448781","url":null,"abstract":"SIAM Journal on Discrete Mathematics, Volume 38, Issue 1, Page 1113-1157, March 2024. <br/> Abstract. In the infinite regular tree [math] with [math], we consider families [math], indexed by vertices [math] and nonnegative integers (“discrete time steps”) [math], of probability measures such that [math] if the distances [math] and [math] are equal. Let [math] be a positive integer, and let [math] and [math] be two vertices in the tree which are at distance [math] apart. We compute a formula for the transportation distance [math] in terms of generating functions. In the special case where [math] are measures from simple random walks after [math] time steps, we establish the linear asymptotic formula [math], as [math], and give the formulas for the coefficients [math] and [math] in closed forms. We also obtain linear asymptotic formulas when [math] is the uniform distribution on the sphere or on the ball of radius [math] as [math]. We show that these six coefficients (two from the simple random walk, two from the uniform distribution on the sphere, and two from the uniform distribution on the ball) are related by inequalities.","PeriodicalId":49530,"journal":{"name":"SIAM Journal on Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140151871","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
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. <br/> 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":null,"pages":null},"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. <br/> 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":null,"pages":null},"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
Don’t Roll the Dice, Ask Twice: The Two-Query Distortion of Matching Problems and Beyond 不要掷骰子，要问两次：匹配问题及其他问题的两次查询失真
IF 0.8 3区 数学
SIAM Journal on Discrete Mathematics Pub Date : 2024-03-12 DOI: 10.1137/23m1545677
Georgios Amanatidis, Georgios Birmpas, Aris Filos-Ratsikas, Alexandros A. Voudouris
{"title":"Don’t Roll the Dice, Ask Twice: The Two-Query Distortion of Matching Problems and Beyond","authors":"Georgios Amanatidis, Georgios Birmpas, Aris Filos-Ratsikas, Alexandros A. Voudouris","doi":"10.1137/23m1545677","DOIUrl":"https://doi.org/10.1137/23m1545677","url":null,"abstract":"SIAM Journal on Discrete Mathematics, Volume 38, Issue 1, Page 1007-1029, March 2024. <br/> Abstract. In most social choice settings, the participating agents express their preferences over the different alternatives in the form of linear orderings. While this clearly simplifies preference elicitation, it inevitably leads to poor performance with respect to optimizing a cardinal objective, such as the social welfare, since the values of the agents remain virtually unknown. This loss in performance because of lack of information is measured by the notion of distortion. A recent array of works put forward the agenda of designing mechanisms that learn the values of the agents for a small number of alternatives via queries, and use this limited extra information to make better-informed decisions, thus improving distortion. Following this agenda, in this work we focus on a class of combinatorial problems that includes most well-known matching problems and several of their generalizations. For problems such as One-Sided Matching, Two-Sided Matching, General Graph Matching, and Short Cycle Packing, we design two-query mechanisms that achieve the best-possible worst-case distortion in terms of social welfare, and outperform the best-possible expected distortion achieved by randomized ordinal mechanisms. Our results extend to problems like [math]-Constrained Resource Allocation, General Graph [math]-Matching, and [math]-Clique Packing, when [math] is restricted to be any constant.","PeriodicalId":49530,"journal":{"name":"SIAM Journal on Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140124938","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
Online Spanners in Metric Spaces 公制空间中的在线施展器
IF 0.8 3区 数学
SIAM Journal on Discrete Mathematics Pub Date : 2024-03-12 DOI: 10.1137/22m1534572
Sujoy Bhore, Arnold Filtser, Hadi Khodabandeh, Csaba D. Tóth
{"title":"Online Spanners in Metric Spaces","authors":"Sujoy Bhore, Arnold Filtser, Hadi Khodabandeh, Csaba D. Tóth","doi":"10.1137/22m1534572","DOIUrl":"https://doi.org/10.1137/22m1534572","url":null,"abstract":"SIAM Journal on Discrete Mathematics, Volume 38, Issue 1, Page 1030-1056, March 2024. <br/> Abstract. Given a metric space [math], a weighted graph [math] over [math] is a metric [math]-spanner of [math] if for every [math], [math], where [math] is the shortest path metric in [math]. In this paper, we construct spanners for finite sets in metric spaces in the online setting. Here, we are given a sequence of points [math], where the points are presented one at a time (i.e., after [math] steps, we see [math]). The algorithm is allowed to add edges to the spanner when a new point arrives; however, it is not allowed to remove any edge from the spanner. The goal is to maintain a [math]-spanner [math] for [math] for all [math], while minimizing the number of edges, and their total weight. We construct online [math]-spanners in the Euclidean [math]-space, [math]-spanners for general metrics, and [math]-spanners for ultrametrics. Most notably, in the Euclidean plane, we construct a [math]-spanner with competitive ratio [math], bypassing the classic lower bound [math] for lightness, which compares the weight of the spanner to that of the minimum spanning tree.","PeriodicalId":49530,"journal":{"name":"SIAM Journal on Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140125215","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 the Concentration of the Maximum Degree in the Duplication-Divergence Models 论重复-发散模型中最大度数的集中问题
IF 0.8 3区 数学
SIAM Journal on Discrete Mathematics Pub Date : 2024-03-07 DOI: 10.1137/23m1592766
Alan M. Frieze, Krzysztof Turowski, Wojciech Szpankowski
{"title":"On the Concentration of the Maximum Degree in the Duplication-Divergence Models","authors":"Alan M. Frieze, Krzysztof Turowski, Wojciech Szpankowski","doi":"10.1137/23m1592766","DOIUrl":"https://doi.org/10.1137/23m1592766","url":null,"abstract":"SIAM Journal on Discrete Mathematics, Volume 38, Issue 1, Page 988-1006, March 2024. <br/> Abstract. We present a rigorous and precise analysis of the maximum degree and the average degree in a dynamic duplication-divergence graph model introduced by Solé et al. [Adv. Complex Syst., 5 (2002), pp. 43–54] in which the graph grows according to a duplication-divergence mechanism, i.e., by iteratively creating a copy of some node and then randomly alternating the neighborhood of a new node with probability [math]. This model captures the growth of some real-world processes, e.g., biological or social networks. In this paper, we prove that for some [math], the maximum degree and the average degree of a duplication-divergence graph on [math] vertices are asymptotically concentrated with high probability around [math] and [math], respectively, i.e., they are within at most a polylogarithmic factor from these values with probability at least [math] for any constant [math].","PeriodicalId":49530,"journal":{"name":"SIAM Journal on Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140057685","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
Treewidth, Circle Graphs, and Circular Drawings 树宽、圆图和圆形图画
IF 0.8 3区 数学
SIAM Journal on Discrete Mathematics Pub Date : 2024-03-06 DOI: 10.1137/22m1542854
Robert Hickingbotham, Freddie Illingworth, Bojan Mohar, David R. Wood
{"title":"Treewidth, Circle Graphs, and Circular Drawings","authors":"Robert Hickingbotham, Freddie Illingworth, Bojan Mohar, David R. Wood","doi":"10.1137/22m1542854","DOIUrl":"https://doi.org/10.1137/22m1542854","url":null,"abstract":"SIAM Journal on Discrete Mathematics, Volume 38, Issue 1, Page 965-987, March 2024. <br/> Abstract. A circle graph is an intersection graph of a set of chords of a circle. We describe the unavoidable induced subgraphs of circle graphs with large treewidth. This includes examples that are far from the “usual suspects.” Our results imply that treewidth and Hadwiger number are linearly tied on the class of circle graphs and that the unavoidable induced subgraphs of a vertex-minor-closed class with large treewidth are the usual suspects if and only if the class has bounded rank-width. Using the same tools, we also study the treewidth of graphs [math] that have a circular drawing whose crossing graph is well-behaved in some way. In this setting, we show that if the crossing graph is [math]-minor-free, then [math] has treewidth at most [math] and has no [math]-topological minor. On the other hand, we show that there are graphs with arbitrarily large Hadwiger number that have circular drawings whose crossing graphs are 2-degenerate.","PeriodicalId":49530,"journal":{"name":"SIAM Journal on Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140044392","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 [math]-Counting of Noncrossing Chains and Parking Functions 论非交叉链的[数学]计数和停车函数
IF 0.8 3区 数学
SIAM Journal on Discrete Mathematics Pub Date : 2024-03-05 DOI: 10.1137/23m1572386
Yen-Jen Cheng, Sen-Peng Eu, Tung-Shan Fu, Jyun-Cheng Yao
{"title":"On [math]-Counting of Noncrossing Chains and Parking Functions","authors":"Yen-Jen Cheng, Sen-Peng Eu, Tung-Shan Fu, Jyun-Cheng Yao","doi":"10.1137/23m1572386","DOIUrl":"https://doi.org/10.1137/23m1572386","url":null,"abstract":"SIAM Journal on Discrete Mathematics, Volume 38, Issue 1, Page 917-946, March 2024. <br/> Abstract. For a finite Coxeter group [math], Josuat-Vergès derived a [math]-polynomial counting the maximal chains in the lattice of noncrossing partitions of [math] by weighting some of the covering relations, which we call bad edges, in these chains with a parameter [math]. We study the connection of these weighted chains with parking functions of type [math] ([math], respectively) from the perspective of the [math]-polynomial. The [math]-polynomial turns out to be the generating function for parking functions (of either type) with respect to the number of cars that do not park in their preferred spaces. In either case, we present a bijective result that carries bad edges to unlucky cars while preserving their relative order. Using this, we give an interpretation of the [math]-positivity of the [math]-polynomial in the case when [math] is the hyperoctahedral group.","PeriodicalId":49530,"journal":{"name":"SIAM Journal on Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-03-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140037687","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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