Graphs and Combinatorics最新文献_第10页

Four-vertex traces of finite sets 有限集的四顶点轨迹

IF 0.7 4区数学

Graphs and Combinatorics Pub Date : 2023-12-23 DOI: 10.1007/s00373-023-02738-5

Peter Frankl, Jian Wang

引用次数: 0

Weak-Dynamic Coloring of Graphs Beyond-Planarity 图形的弱动态着色超越平面性

IF 0.7 4区数学

Graphs and Combinatorics Pub Date : 2023-12-23 DOI: 10.1007/s00373-023-02733-w

Weichan Liu, Guiying Yan

引用次数: 0

The Maximum 4-Vertex-Path Packing of a Cubic Graph Covers At Least Two-Thirds of Its Vertices 立方图的最大 4 顶点路径包装至少覆盖三分之二的顶点

IF 0.7 4区数学

Graphs and Combinatorics Pub Date : 2023-12-20 DOI: 10.1007/s00373-023-02732-x

引用次数: 0

Turán Numbers of Several Bipartite Graphs 多个二方图的图兰数

IF 0.7 4区数学

Graphs and Combinatorics Pub Date : 2023-12-14 DOI: 10.1007/s00373-023-02731-y

Ye Wang, Yusheng Li, Yan Li

引用次数: 0

Tashkinov-Trees: An Annotated Proof 塔什金诺夫树注释证明

IF 0.7 4区数学

Graphs and Combinatorics Pub Date : 2023-12-14 DOI: 10.1007/s00373-023-02712-1

András Sebő

{"title":"Tashkinov-Trees: An Annotated Proof","authors":"András Sebő","doi":"10.1007/s00373-023-02712-1","DOIUrl":"https://doi.org/10.1007/s00373-023-02712-1","url":null,"abstract":"Tashkinov-trees have been used as a tool for proving bounds on the chromatic index, and are becoming a fundamental tool for edge-coloring. Was its publication in a language different from English an obstacle for the accessibility of a clean and complete proof of Tashkinov’s fundamental theorem? Tashkinov’s original, Russian paper offers a clear presentation of this theorem and its proof. The theorem itself has been well understood and successfully applied, but the proof is more difficult. It builds a truly amazing recursive machine, where the various cases necessitate a refined and polished analysis to fit into one another with surprising smoothness and accuracy. The difficulties were brilliantly unknotted by the author, deserving repeated attention. The present work is the result of reading, translating, reorganizing, rewriting, completing, shortcutting and annotating Tashkinov’s proof. It is essentially the same proof, with non-negligeable communicational differences though, for instance completing it wherever it occurred to be necessary, and simplifying it whenever it appeared to be possible, at the same time trying to adapt it to the habits and taste of the international graph theory community.","PeriodicalId":12811,"journal":{"name":"Graphs and Combinatorics","volume":"32 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138684207","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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 Turán Number of $$K_m vee C_{2k-1}$$ 在Turán的数量 $$K_m vee C_{2k-1}$$

IF 0.7 4区数学

Graphs and Combinatorics Pub Date : 2023-12-04 DOI: 10.1007/s00373-023-02728-7

Jingru Yan

引用次数: 0

Cographs and 1-Sums 图与1-和

IF 0.7 4区数学

Graphs and Combinatorics Pub Date : 2023-12-04 DOI: 10.1007/s00373-023-02730-z

Jagdeep Singh

引用次数: 0

$$l_{1}$$ -embeddability of shifted quadrilateral cylinder graphs $$l_{1}$$ 移位四边形柱面图的可嵌入性

IF 0.7 4区数学

Graphs and Combinatorics Pub Date : 2023-11-29 DOI: 10.1007/s00373-023-02725-w

Guangfu Wang, Zhikun Xiong, Lijun Chen

引用次数: 0

Complexity of Total Dominator Coloring in Graphs 图中总支配子着色的复杂性

IF 0.7 4区数学

Graphs and Combinatorics Pub Date : 2023-11-28 DOI: 10.1007/s00373-023-02726-9

Michael A. Henning, Kusum, Arti Pandey, Kaustav Paul

{"title":"Complexity of Total Dominator Coloring in Graphs","authors":"Michael A. Henning, Kusum, Arti Pandey, Kaustav Paul","doi":"10.1007/s00373-023-02726-9","DOIUrl":"https://doi.org/10.1007/s00373-023-02726-9","url":null,"abstract":"Let (G=(V,E)) be a graph with no isolated vertices. A vertex v totally dominates a vertex w ((w ne v)), if v is adjacent to w. A set (D subseteq V) called a total dominating set of G if every vertex (vin V) is totally dominated by some vertex in D. The minimum cardinality of a total dominating set is the total domination number of G and is denoted by (gamma _t(G)). A total dominator coloring of graph G is a proper coloring of vertices of G, so that each vertex totally dominates some color class. The total dominator chromatic number (chi _{{textrm{td}}}(G)) of G is the least number of colors required for a total dominator coloring of G. The Total Dominator Coloring problem is to find a total dominator coloring of G using the minimum number of colors. It is known that the decision version of this problem is NP-complete for general graphs. We show that it remains NP-complete even when restricted to bipartite, planar and split graphs. We further study the Total Dominator Coloring problem for various graph classes, including trees, cographs and chain graphs. First, we characterize the trees having (chi _{{textrm{td}}}(T)=gamma _t(T)+1), which completes the characterization of trees achieving all possible values of (chi _{{textrm{td}}}(T)). Also, we show that for a cograph G, (chi _{{textrm{td}}}(G)) can be computed in linear-time. Moreover, we show that (2 le chi _{{textrm{td}}}(G) le 4) for a chain graph G and then we characterize the class of chain graphs for every possible value of (chi _{{textrm{td}}}(G)) in linear-time.","PeriodicalId":12811,"journal":{"name":"Graphs and Combinatorics","volume":"72 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138530250","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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

Variable Degeneracy on Toroidal Graphs 环面图上的变量简并

IF 0.7 4区数学

Graphs and Combinatorics Pub Date : 2023-11-23 DOI: 10.1007/s00373-023-02721-0

Rui Li, Tao Wang

{"title":"Variable Degeneracy on Toroidal Graphs","authors":"Rui Li, Tao Wang","doi":"10.1007/s00373-023-02721-0","DOIUrl":"https://doi.org/10.1007/s00373-023-02721-0","url":null,"abstract":"DP-coloring was introduced by Dvořák and Postle as a generalization of list coloring and signed coloring. A new coloring, strictly f-degenerate transversal, is a further generalization of DP-coloring and L-forested-coloring. In this paper, we present some structural results on planar and toroidal graphs with forbidden configurations, and establish some sufficient conditions for the existence of strictly f-degenerate transversal based on these structural results. Consequently, (i) every toroidal graph without subgraphs in Fig. 2 is DP-4-colorable, and has list vertex arboricity at most 2, (ii) every toroidal graph without 4-cycles is DP-4-colorable, and has list vertex arboricity at most 2, (iii) every planar graph without subgraphs isomorphic to the configurations in Fig. 3 is DP-4-colorable, and has list vertex arboricity at most 2. These results improve upon previous results on DP-4-coloring (Kim and Ozeki in Discrete Math 341(7):1983–1986. https://doi.org/10.1016/j.disc.2018.03.027, 2018; Sittitrai and Nakprasit in Bull Malays Math Sci Soc 43(3):2271–2285. https://doi.org/10.1007/s40840-019-00800-1, 2020) and (list) vertex arboricity (Choi and Zhang in Discrete Math 333:101–105. https://doi.org/10.1016/j.disc.2014.06.011, 2014; Huang et al. in Int J Math Stat 16(1):97–105, 2015; Zhang in Iranian Math Soc 42(5):1293–1303, 2016).","PeriodicalId":12811,"journal":{"name":"Graphs and Combinatorics","volume":"39 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-11-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138530252","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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: 2