SIAM Journal on Discrete Mathematics最新文献

英文中文

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 Q2 MATHEMATICS

SIAM Journal on Discrete Mathematics

Pub Date : 2024-03-12 DOI: 10.1137/23m1545677

Georgios Amanatidis, Georgios Birmpas, Aris Filos-Ratsikas, Alexandros A. Voudouris

SIAM Journal on Discrete Mathematics, Volume 38, Issue 1, Page 1007-1029, March 2024.
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.

SIAM 离散数学杂志》，第 38 卷第 1 期，第 1007-1029 页，2024 年 3 月。摘要在大多数社会选择环境中，参与的代理人以线性排序的形式表达他们对不同备选方案的偏好。虽然这明显简化了偏好激发，但却不可避免地导致在优化诸如社会福利之类的有意义目标时表现不佳，因为参与者的价值观几乎是未知的。这种因缺乏信息而造成的绩效损失可以用失真概念来衡量。最近的一系列工作提出了这样一个议程，即设计一种机制，通过查询了解代理对少量备选方案的价值，并利用这些有限的额外信息做出更明智的决策，从而改善失真。根据这一议程，我们在这项工作中将重点放在一类组合问题上，其中包括大多数众所周知的匹配问题及其一些泛化问题。对于单面匹配、双面匹配、一般图匹配和短周期打包等问题，我们设计的双查询机制在社会福利方面实现了最佳的最坏情况失真，并优于随机序数机制实现的最佳预期失真。当[math]被限制为任意常数时，我们的结果可以扩展到[math]-受限资源分配、一般图[math]-匹配和[math]-斜线打包等问题。

{"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":"36 1","pages":""},"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 Q2 MATHEMATICS

SIAM Journal on Discrete Mathematics

Pub Date : 2024-03-12 DOI: 10.1137/22m1534572

Sujoy Bhore, Arnold Filtser, Hadi Khodabandeh, Csaba D. Tóth

SIAM Journal on Discrete Mathematics, Volume 38, Issue 1, Page 1030-1056, March 2024.
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.

SIAM 离散数学杂志》，第 38 卷，第 1 期，第 1030-1056 页，2024 年 3 月。摘要。给定一个度量空间[math]，如果对于每一个[math]，[math]，其中[math]是[math]中的最短路径度量，则[math]上的加权图[math]是[math]的度量[math]-spanner。在本文中，我们将在在线设置中为度量空间中的有限集构建spanner。在这里，我们给定了一个点序列 [math]，点是一个一个呈现的（即在 [math] 步之后，我们看到 [math]）。当有新的点出现时，算法可以在[spanner]中添加边；但不允许从[spanner]中移除任何边。我们的目标是为[math]的所有[math]保持一个[math]-spanner[math]，同时最大限度地减少边的数量及其总权重。我们构建了欧氏[math]空间的在线[math]扫描器、一般度量的[math]扫描器和超度量的[math]扫描器。最值得注意的是，在欧几里得平面上，我们构建了一个具有竞争比[math]的[math]扫描器，绕过了经典的轻度下限[math]，它将扫描器的权重与最小生成树的权重进行了比较。

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 Q2 MATHEMATICS

SIAM Journal on Discrete Mathematics

Pub Date : 2024-03-07 DOI: 10.1137/23m1592766

Alan M. Frieze, Krzysztof Turowski, Wojciech Szpankowski

SIAM Journal on Discrete Mathematics, Volume 38, Issue 1, Page 988-1006, March 2024.
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].

SIAM 离散数学杂志》第 38 卷第 1 期第 988-1006 页，2024 年 3 月。摘要。我们对 Solé 等人[Adv. Complex Syst.，5 (2002)，pp. 43-54] 提出的动态复制-发散图模型中的最大度和平均度进行了严格而精确的分析。这一模型捕捉到了现实世界中某些过程的增长，如生物或社会网络。在本文中，我们证明了对于某些[math]，[math]顶点上的复制-发散图的最大度和平均度分别以很高的概率渐近地集中在[math]和[math]附近，也就是说，对于任意常数[math]，它们与这些值的距离最多在一个多项式因子之内，概率至少为[math]。

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 Q2 MATHEMATICS

SIAM Journal on Discrete Mathematics

Pub Date : 2024-03-06 DOI: 10.1137/22m1542854

Robert Hickingbotham, Freddie Illingworth, Bojan Mohar, David R. Wood

SIAM Journal on Discrete Mathematics, Volume 38, Issue 1, Page 965-987, March 2024.
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.

SIAM 离散数学杂志》第 38 卷第 1 期第 965-987 页，2024 年 3 月。摘要圆图是圆的弦集的交集图。我们描述了具有大树宽的圆图不可避免的诱导子图。其中包括一些与 "常见图 "相去甚远的例子。我们的结果意味着，树宽和哈德维格数在圆图类上是线性关系，并且如果且仅如果具有大树宽的顶点-小封闭类具有有界的秩宽，则该类不可避免的诱导子图就是 "惯常嫌疑犯"。利用同样的工具，我们还研究了具有圆形图的图的树宽[math]，这些图的交叉图在某种程度上是良好的。在这种情况下，我们证明，如果交叉图是无[math]次要的，那么[math]的树宽至多为[math]，并且没有[math]拓扑次要。另一方面，我们证明了存在具有任意大的哈德维格数的图，这些图具有圆形图画，其交叉图是 2-退化的。

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 Q2 MATHEMATICS

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

SIAM Journal on Discrete Mathematics, Volume 38, Issue 1, Page 917-946, March 2024.
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.

SIAM 离散数学杂志》，第 38 卷，第 1 期，第 917-946 页，2024 年 3 月。摘要。对于有限 Coxeter 群 [math]，Josuat-Vergès 通过对这些链中的一些覆盖关系（我们称之为坏边）用一个参数[math]加权，推导出了一个[math]多项式，用于计算[math]非交叉分区晶格中的最大链。我们分别从[math]-polynomial 的角度来研究这些加权链与[math]（[math]）类型停车函数的联系。结果表明，[math]-polynomial 是停车函数（无论哪种类型）的生成函数，与没有停在首选车位的汽车数量有关。在这两种情况下，我们都提出了一个双射结果，即在保持相对顺序的情况下，将坏边带到不走运的汽车上。利用这一点，我们给出了当[math]是高八面体群时，[math]多项式的[math]正向性的解释。

引用次数: 0

Eigenpolytope Universality and Graphical Designs 特征多面体普遍性和图形设计

IF 0.8 3区数学 Q2 MATHEMATICS

SIAM Journal on Discrete Mathematics

Pub Date : 2024-03-05 DOI: 10.1137/22m1528768

Catherine Babecki, David Shiroma

SIAM Journal on Discrete Mathematics, Volume 38, Issue 1, Page 947-964, March 2024.
Abstract. We show that the eigenpolytopes of graphs are universal in the sense that every polytope, up to affine equivalence, appears as the eigenpolytope of some positively weighted graph. We next extend the theory of graphical designs, which are quadrature rules for graphs, to positively weighted graphs. Through Gale duality for polytopes, we show a bijection between graphical designs and the faces of eigenpolytopes. This bijection proves the existence of graphical designs with positive quadrature weights and upper bounds the size of a minimal graphical design. Connecting this bijection with the universality of eigenpolytopes, we establish three complexity results: It is strongly NP-complete to determine if there is a graphical design smaller than the mentioned upper bound, it is NP-hard to find a smallest graphical design, and it is #P-complete to count the number of minimal graphical designs.

SIAM 离散数学杂志》，第 38 卷，第 1 期，第 947-964 页，2024 年 3 月。摘要我们证明了图的特征多面体是普适的，即每个多面体（直到仿射等价）都是某个正向加权图的特征多面体。接下来，我们将图形设计理论（即图形的正交规则）扩展到正加权图形。通过多面体的盖尔对偶性，我们展示了图形设计与特征多面体的面之间的双射关系。这个偏射证明了具有正二次权重的图形设计的存在，并给出了最小图形设计的大小上限。将这一偏射与特征多面体的普遍性联系起来，我们建立了三个复杂性结果：确定是否存在小于上述上限的图形设计是强 NP-完全的，找到最小图形设计是 NP-困难的，计算最小图形设计的数量是 #P- 完全的。

引用次数: 0

Robust Factorizations and Colorings of Tensor Graphs 张量图的稳健因式分解和着色

IF 0.8 3区数学 Q2 MATHEMATICS

SIAM Journal on Discrete Mathematics

Pub Date : 2024-02-28 DOI: 10.1137/23m1552474

Joshua Brakensiek, Sami Davies

SIAM Journal on Discrete Mathematics, Volume 38, Issue 1, Page 883-916, March 2024.
Abstract. Since the seminal result of Karger, Motwani, and Sudan, algorithms for approximate 3-coloring have primarily centered around rounding the solution to a Semidefinite Program. However, it is likely that important combinatorial or algebraic insights are needed in order to break the [math] threshold. One way to develop new understanding in graph coloring is to study special subclasses of graphs. For instance, Blum studied the 3-coloring of random graphs, and Arora and Ge studied the 3-coloring of graphs with low threshold-rank. In this work, we study graphs that arise from a tensor product, which appear to be novel instances of the 3-coloring problem. We consider graphs of the form [math] with [math] and [math], where [math] is any edge set such that no vertex has more than an [math]-fraction of its edges in [math]. We show that one can construct [math] with [math] that is close to [math]. For arbitrary [math], [math] satisfies [math]. Additionally, when [math] is a mild expander, we provide a 3-coloring for [math] in polynomial time. These results partially generalize an exact tensor factorization algorithm of Imrich. On the other hand, without any assumptions on [math], we show that it is NP-hard to 3-color [math].

SIAM 离散数学杂志》，第 38 卷，第 1 期，第 883-916 页，2024 年 3 月。摘要。自从 Karger、Motwani 和 Sudan 的开创性成果问世以来，近似 3-着色的算法主要围绕半定式程序解的四舍五入展开。然而，要突破[数学]门槛，很可能需要重要的组合或代数见解。发展对图形着色新理解的一种方法是研究特殊的图形子类。例如，Blum 研究了随机图的 3 着色，Arora 和 Ge 研究了低阈值等级图的 3 着色。在这项工作中，我们研究的是由张量乘积产生的图，这似乎是 3 着色问题的新实例。我们考虑[math]与[math]和[math]的[math]形式的图，其中[math]是任意边集，使得没有顶点在[math]中的边超过[math]的分数。我们证明，我们可以用[math]构造出接近[math]的[math]。对于任意 [math]，[math] 满足 [math]。此外，当 [math] 是一个温和的扩展器时，我们可以在多项式时间内为 [math] 提供一个 3 色。这些结果部分推广了伊姆里奇的精确张量因式分解算法。另一方面，在不对[math]做任何假设的情况下，我们证明了对[math]进行 3 着色是 NP 难的。

{"title":"Robust Factorizations and Colorings of Tensor Graphs","authors":"Joshua Brakensiek, Sami Davies","doi":"10.1137/23m1552474","DOIUrl":"https://doi.org/10.1137/23m1552474","url":null,"abstract":"SIAM Journal on Discrete Mathematics, Volume 38, Issue 1, Page 883-916, March 2024. <br/> Abstract. Since the seminal result of Karger, Motwani, and Sudan, algorithms for approximate 3-coloring have primarily centered around rounding the solution to a Semidefinite Program. However, it is likely that important combinatorial or algebraic insights are needed in order to break the [math] threshold. One way to develop new understanding in graph coloring is to study special subclasses of graphs. For instance, Blum studied the 3-coloring of random graphs, and Arora and Ge studied the 3-coloring of graphs with low threshold-rank. In this work, we study graphs that arise from a tensor product, which appear to be novel instances of the 3-coloring problem. We consider graphs of the form [math] with [math] and [math], where [math] is any edge set such that no vertex has more than an [math]-fraction of its edges in [math]. We show that one can construct [math] with [math] that is close to [math]. For arbitrary [math], [math] satisfies [math]. Additionally, when [math] is a mild expander, we provide a 3-coloring for [math] in polynomial time. These results partially generalize an exact tensor factorization algorithm of Imrich. On the other hand, without any assumptions on [math], we show that it is NP-hard to 3-color [math].","PeriodicalId":49530,"journal":{"name":"SIAM Journal on Discrete Mathematics","volume":"109 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140009282","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 Spanning Trees in Randomly Colored [math] 随机彩色彩虹生成树[数学］

IF 0.8 3区数学 Q2 MATHEMATICS

SIAM Journal on Discrete Mathematics

Pub Date : 2024-02-27 DOI: 10.1137/22m1537497

Deepak Bal, Alan Frieze, Paweł Prałat

SIAM Journal on Discrete Mathematics, Volume 38, Issue 1, Page 867-882, March 2024.
Abstract. Given a graph [math] on [math] vertices and an assignment of colors to its edges, a set of edges [math] is said to be rainbow if edges from [math] have pairwise different colors assigned to them. In this paper, we investigate rainbow spanning trees in randomly colored random [math] graphs.

SIAM 离散数学杂志》，第 38 卷，第 1 期，第 867-882 页，2024 年 3 月。摘要。给定[math]顶点上的图[math]及其边的颜色赋值，如果[math]中的边有成对的不同颜色赋值，则称一组边[math]为彩虹边。本文研究了随机颜色随机 [math] 图中的彩虹生成树。

引用次数: 0

Pathwidth Versus Cocircumference 路径宽度与头围

IF 0.8 3区数学 Q2 MATHEMATICS

SIAM Journal on Discrete Mathematics

Pub Date : 2024-02-26 DOI: 10.1137/23m158663x

Marcin Briański, Gwenaël Joret, Michał T. Seweryn

SIAM Journal on Discrete Mathematics, Volume 38, Issue 1, Page 857-866, March 2024.
Abstract. The circumference of a graph [math] with at least one cycle is the length of a longest cycle in [math]. A classic result of Birmelé [J. Graph Theory, 43 (2003), pp. 24–25] states that the treewidth of [math] is at most its circumference minus 1. In case [math] is 2-connected, this upper bound also holds for the pathwidth of [math]; in fact, even the treedepth of [math] is upper bounded by its circumference (Briański et al. [Treedepth vs circumference, Combinatorica, 43 (2023), pp. 659–664]). In this paper, we study whether similar bounds hold when replacing the circumference of [math] by its cocircumference, defined as the largest size of a bond in [math], an inclusionwise minimal set of edges [math] such that [math] has more components than [math]. In matroidal terms, the cocircumference of [math] is the circumference of the bond matroid of [math]. Our first result is the following “dual” version of Birmelé’s theorem: The treewidth of a graph [math] is at most its cocircumference. Our second and main result is an upper bound of [math] on the pathwidth of a 2-connected graph [math] with cocircumference [math]. Contrary to circumference, no such bound holds for the treedepth of [math]. Our two upper bounds are best possible up to a constant factor.

SIAM 离散数学杂志》，第 38 卷第 1 期，第 857-866 页，2024 年 3 月。摘要。至少有一个循环的图[math]的周长是[math]中最长循环的长度。Birmelé [J. Graph Theory, 43 (2003), pp. 24-25] 的一个经典结果指出，[math] 的树宽最多为周长减 1。如果[math]是 2 连接的，那么[math]的路径宽度也有这个上界；事实上，甚至[math]的树深也有其周长的上界（Briański 等人 [Treedepth vs circumference, Combinatorica, 43 (2023), pp. 659-664]）。在本文中，我们将研究当用[math]的cocircumference 代替[math]的周长时，类似的边界是否成立。cocircumference 的定义是[math]中一个结合点的最大尺寸，它是边[math]的包容最小集，使得[math]的成分多于[math]。用母陀螺术语来说，[math] 的cocircumference 就是[math] 的bond matroid 的周长。我们的第一个结果是以下伯梅莱定理的 "对偶 "版本：一个图[math]的树宽最多是它的cocircumference。我们的第二个也是主要的结果是[math]关于具有圆周率[math]的 2 连接图[math]的路径宽度的上界[math]。与圆周率相反，[math] 的树深度不存在这样的上界。我们的两个上界在一个常数因子以内都是最好的。

{"title":"Pathwidth Versus Cocircumference","authors":"Marcin Briański, Gwenaël Joret, Michał T. Seweryn","doi":"10.1137/23m158663x","DOIUrl":"https://doi.org/10.1137/23m158663x","url":null,"abstract":"SIAM Journal on Discrete Mathematics, Volume 38, Issue 1, Page 857-866, March 2024. <br/> Abstract. The circumference of a graph [math] with at least one cycle is the length of a longest cycle in [math]. A classic result of Birmelé [J. Graph Theory, 43 (2003), pp. 24–25] states that the treewidth of [math] is at most its circumference minus 1. In case [math] is 2-connected, this upper bound also holds for the pathwidth of [math]; in fact, even the treedepth of [math] is upper bounded by its circumference (Briański et al. [Treedepth vs circumference, Combinatorica, 43 (2023), pp. 659–664]). In this paper, we study whether similar bounds hold when replacing the circumference of [math] by its cocircumference, defined as the largest size of a bond in [math], an inclusionwise minimal set of edges [math] such that [math] has more components than [math]. In matroidal terms, the cocircumference of [math] is the circumference of the bond matroid of [math]. Our first result is the following “dual” version of Birmelé’s theorem: The treewidth of a graph [math] is at most its cocircumference. Our second and main result is an upper bound of [math] on the pathwidth of a 2-connected graph [math] with cocircumference [math]. Contrary to circumference, no such bound holds for the treedepth of [math]. Our two upper bounds are best possible up to a constant factor.","PeriodicalId":49530,"journal":{"name":"SIAM Journal on Discrete Mathematics","volume":"27 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139979291","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

Cops and Robbers on [math]-Free Graphs 无[数学]图形上的警察与强盗

IF 0.8 3区数学 Q2 MATHEMATICS

SIAM Journal on Discrete Mathematics

Pub Date : 2024-02-26 DOI: 10.1137/23m1549912

Maria Chudnovsky, Sergey Norin, Paul D. Seymour, Jérémie Turcotte

SIAM Journal on Discrete Mathematics, Volume 38, Issue 1, Page 845-856, March 2024.
Abstract. We prove that every connected [math]-free graph has cop number at most two, solving a conjecture of Sivaraman. In order to do so, we first prove that every connected [math]-free graph [math] with independence number at least three contains a three-vertex induced path with vertices [math] in order, such that every neighbor of [math] is also adjacent to one of [math].

SIAM 离散数学杂志》，第 38 卷，第 1 期，第 845-856 页，2024 年 3 月。摘要。我们证明了每一个连通的无[数学]图的 cop 数最多只有两个，从而解决了 Sivaraman 的一个猜想。为此，我们首先证明，每一个独立数至少为三的连通无[math]图[math]都包含一条顶点[math]按顺序排列的三顶点诱导路径，使得[math]的每一个邻接点都与[math]的一个邻接点相邻。

引用次数: 0

首页上一页

下一页尾页

类型

全部化学•材料生命科学医学物理工程技术环境•农林材料科学地球科学法学管理学化学环境科学与生态学计算机科学教育学经济学农林科学人文科学生物学数学物理与天体物理心理学综合性期刊其他工业工程理学历史学农学文学信息工程

数据库

全部 ACS Publications Elsevier ieeexplore Springer The Royal Society of Chemistry Wiley

期刊

SIAM Journal on Discrete Mathematics

全部 Acc. Chem. Res. ACS Applied Bio Materials ACS Appl. Electron. Mater. ACS Appl. Energy Mater. ACS Appl. Mater. Interfaces ACS Appl. Nano Mater. ACS Appl. Polym. Mater. ACS BIOMATER-SCI ENG ACS Catal. ACS Cent. Sci. ACS Chem. Biol. ACS Chemical Health & Safety ACS Chem. Neurosci. ACS Comb. Sci. ACS Earth Space Chem. ACS Energy Lett. ACS Infect. Dis. ACS Macro Lett. ACS Mater. Lett. ACS Med. Chem. Lett. ACS Nano ACS Omega ACS Photonics ACS Sens. ACS Sustainable Chem. Eng. ACS Synth. Biol. Anal. Chem. BIOCHEMISTRY-US Bioconjugate Chem. BIOMACROMOLECULES Chem. Res. Toxicol. Chem. Rev. Chem. Mater. CRYST GROWTH DES ENERG FUEL Environ. Sci. Technol. Environ. Sci. Technol. Lett. Eur. J. Inorg. Chem. IND ENG CHEM RES Inorg. Chem. J. Agric. Food. Chem. J. Chem. Eng. Data J. Chem. Educ. J. Chem. Inf. Model. J. Chem. Theory Comput. J. Med. Chem. J. Nat. Prod. J PROTEOME RES J. Am. Chem. Soc. LANGMUIR MACROMOLECULES Mol. Pharmaceutics Nano Lett. Org. Lett. ORG PROCESS RES DEV ORGANOMETALLICS J. Org. Chem. J. Phys. Chem. J. Phys. Chem. A J. Phys. Chem. B J. Phys. Chem. C J. Phys. Chem. Lett. Analyst Anal. Methods Biomater. Sci. Catal. Sci. Technol. Chem. Commun. Chem. Soc. Rev. CHEM EDUC RES PRACT CRYSTENGCOMM Dalton Trans. Energy Environ. Sci. ENVIRON SCI-NANO ENVIRON SCI-PROC IMP ENVIRON SCI-WAT RES Faraday Discuss. Food Funct. Green Chem. Inorg. Chem. Front. Integr. Biol. J. Anal. At. Spectrom. J. Mater. Chem. A J. Mater. Chem. B J. Mater. Chem. C Lab Chip Mater. Chem. Front. Mater. Horiz. MEDCHEMCOMM Metallomics Mol. Biosyst. Mol. Syst. Des. Eng. Nanoscale Nanoscale Horiz. Nat. Prod. Rep. New J. Chem. Org. Biomol. Chem. Org. Chem. Front. PHOTOCH PHOTOBIO SCI PCCP Polym. Chem.

﹀