SIAM J. Discret. Math.最新文献_第8页

The Degrees of Regular Polytopes of Type [4, 4, 4] 类型[4,4,4]的正多面体的度

SIAM J. Discret. Math. Pub Date : 2022-05-19 DOI: 10.1137/20m1375012

Maria Elisa Fernandes, Claudio Alexandre Piedade

引用次数: 1

The mixed search game against an agile and visible fugitive is monotone 针对一个敏捷且可见的逃犯的混合搜索游戏是单调的

SIAM J. Discret. Math. Pub Date : 2022-04-22 DOI: 10.48550/arXiv.2204.10691

Guillaume Mescoff, C. Paul, D. Thilikos

{"title":"The mixed search game against an agile and visible fugitive is monotone","authors":"Guillaume Mescoff, C. Paul, D. Thilikos","doi":"10.48550/arXiv.2204.10691","DOIUrl":"https://doi.org/10.48550/arXiv.2204.10691","url":null,"abstract":"We consider the mixed search game against an agile and visible fugitive. This is the variant of the classic fugitive search game on graphs where searchers may be placed to (or removed from) the vertices or slide along edges. Moreover, the fugitive resides on the edges of the graph and can move at any time along unguarded paths. The mixed search number against an agile and visible fugitive of a graph $G$, denoted $avms(G)$, is the minimum number of searchers required to capture to fugitive in this graph searching variant. Our main result is that this graph searching variant is monotone in the sense that the number of searchers required for a successful search strategy does not increase if we restrict the search strategies to those that do not permit the fugitive to visit an already clean edge. This means that mixed search strategies against an agile and visible fugitive can be polynomially certified, and therefore that the problem of deciding, given a graph $G$ and an integer $k,$ whether $avms(G)leq k$ is in NP. Our proof is based on the introduction of the notion of tight bramble, that serves as an obstruction for the corresponding search parameter. Our results imply that for a graph $G$, $avms(G)$ is equal to the Cartesian tree product number of $G$ that is the minimum $k$ for which $G$ is a minor of the Cartesian product of a tree and a clique on $k$ vertices.","PeriodicalId":21749,"journal":{"name":"SIAM J. Discret. Math.","volume":"28 1","pages":"113345"},"PeriodicalIF":0.0,"publicationDate":"2022-04-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87136241","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 1

Lengths of Cycles in Generalized Pancake Graphs 广义煎饼图中圈的长度

SIAM J. Discret. Math. Pub Date : 2022-04-22 DOI: 10.48550/arXiv.2204.10494

Saúl A. Blanco, Charles Buehrle

{"title":"Lengths of Cycles in Generalized Pancake Graphs","authors":"Saúl A. Blanco, Charles Buehrle","doi":"10.48550/arXiv.2204.10494","DOIUrl":"https://doi.org/10.48550/arXiv.2204.10494","url":null,"abstract":"In this paper, we consider the lengths of cycles that can be embedded on the edges of the generalized pancake graphs which are the Cayley graph of the generalized symmetric group $S(m,n)$, generated by prefix reversals. The generalized symmetric group $S(m,n)$ is the wreath product of the cyclic group of order $m$ and the symmetric group of order $n!$. Our main focus is the underlying emph{undirected} graphs, denoted by $mathbb{P}_m(n)$. In the cases when the cyclic group has one or two elements, these graphs are isomorphic to the pancake graphs and burnt pancake graphs, respectively. We prove that when the cyclic group has three elements, $mathbb{P}_3(n)$ has cycles of all possible lengths, thus resembling a similar property of pancake graphs and burnt pancake graphs. Moreover, $mathbb{P}_4(n)$ has all the even-length cycles. We utilize these results as base cases and show that if $m>2$ is even, $mathbb{P}_m(n)$ has all cycles of even length starting from its girth to a Hamiltonian cycle. Moreover, when $m>2$ is odd, $mathbb{P}_m(n)$ has cycles of all lengths starting from its girth to a Hamiltonian cycle. We furthermore show that the girth of $mathbb{P}_m(n)$ is $min{m,6}$ if $mgeq3$, thus complementing the known results for $m=1,2.$","PeriodicalId":21749,"journal":{"name":"SIAM J. Discret. Math.","volume":"27 1","pages":"113624"},"PeriodicalIF":0.0,"publicationDate":"2022-04-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87537392","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 1

Clean Clutters and Dyadic Fractional Packings 清洁杂乱和二元分式填料

SIAM J. Discret. Math. Pub Date : 2022-04-19 DOI: 10.1137/21m1397325

Ahmad Abdi, G. Cornuéjols, B. Guenin, L. Tunçel

引用次数: 6

On strong avoiding games 关于强回避游戏

SIAM J. Discret. Math. Pub Date : 2022-04-17 DOI: 10.48550/arXiv.2204.07971

Milovs Stojakovi'c, Jelena Stratijev

引用次数: 0

Spectral Radius on Linear $r$-Graphs without Expanded $K_{r+1}$ 未展开$K_{r+1}$的线性$r$-图的谱半径

SIAM J. Discret. Math. Pub Date : 2022-04-14 DOI: 10.1137/21m1404740

Guorong Gao, A. Chang, Yuan Hou

引用次数: 11

Revisiting and Improving Upper Bounds for Identifying Codes 对识别码上界的重新审视与改进

SIAM J. Discret. Math. Pub Date : 2022-04-11 DOI: 10.1137/22M148999X

Florent Foucaud, Tuomo Lehtilä

{"title":"Revisiting and Improving Upper Bounds for Identifying Codes","authors":"Florent Foucaud, Tuomo Lehtilä","doi":"10.1137/22M148999X","DOIUrl":"https://doi.org/10.1137/22M148999X","url":null,"abstract":"An identifying code $C$ of a graph $G$ is a dominating set of $G$ such that any two distinct vertices of $G$ have distinct closed neighbourhoods within $C$. These codes have been widely studied for over two decades. We give an improvement over all the best known upper bounds, some of which have stood for over 20 years, for identifying codes in trees, proving the upper bound of $(n+ell)/2$, where $n$ is the order and $ell$ is the number of leaves (pendant vertices) of the graph. In addition to being an improvement in size, the new upper bound is also an improvement in generality, as it actually holds for bipartite graphs having no twins (pairs of vertices with the same closed or open neighbourhood) of degree 2 or greater. We also show that the bound is tight for an infinite class of graphs and that there are several structurally different families of trees attaining the bound. We then use our bound to derive a tight upper bound of $2n/3$ for twin-free bipartite graphs of order $n$, and characterize the extremal examples, as $2$-corona graphs of bipartite graphs. This is best possible, as there exist twin-free graphs, and trees with twins, that need $n-1$ vertices in any of their identifying codes. We also generalize the existing upper bound of $5n/7$ for graphs of order $n$ and girth at least 5 when there are no leaves, to the upper bound $frac{5n+2ell}{7}$ when leaves are allowed. This is tight for the $7$-cycle $C_7$ and for all stars.","PeriodicalId":21749,"journal":{"name":"SIAM J. Discret. Math.","volume":"26 1","pages":"2619-2634"},"PeriodicalIF":0.0,"publicationDate":"2022-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73933633","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 4

Counting and Cutting Rich Lenses in Arrangements of Circles 在圆的排列中计数和切割丰富的透镜

SIAM J. Discret. Math. Pub Date : 2022-04-11 DOI: 10.1137/21m1409305

Esther Ezra, O. Raz, M. Sharir, Joshua Zahl

引用次数: 0

A Fixed-Parameter Tractable Algorithm for Elimination Distance to Bounded Degree Graphs 有界度图距离消去的一种固定参数可处理算法

SIAM J. Discret. Math. Pub Date : 2022-04-07 DOI: 10.1137/21m1396824

A. Agrawal, Lawqueen Kanesh, Fahad Panolan, M. Ramanujan, Saket Saurabh

引用次数: 0

Covering projective planar graphs with three forests 用三个森林覆盖投影平面图

SIAM J. Discret. Math. Pub Date : 2022-04-01 DOI: 10.1016/j.disc.2021.112748

Raiji Mukae, K. Ozeki, Terukazu Sano, Ryuji Tazume

引用次数: 0