Graphs and Combinatorics最新文献_第6页

A Matrix for Counting Paths in Acyclic Colored Digraphs 无环彩色图中的路径计数矩阵

IF 0.7 4区数学

Graphs and Combinatorics Pub Date : 2024-04-08 DOI: 10.1007/s00373-024-02785-6

Sudip Bera

引用次数: 0

The primality graph of critical 3-hypergraphs 临界 3-hypergraph 的基元图

IF 0.7 4区数学

Graphs and Combinatorics Pub Date : 2024-04-06 DOI: 10.1007/s00373-024-02772-x

引用次数: 0

On the Edge-Erdős–Pósa Property of Ladders 关于梯子的边缘-厄尔多斯-波萨特性

IF 0.7 4区数学

Graphs and Combinatorics Pub Date : 2024-04-05 DOI: 10.1007/s00373-024-02765-w

Raphael Steck, Arthur Ulmer

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Planar Graphs with the Maximum Number of Induced 4-Cycles or 5-Cycles 具有最多诱导 4 周期或 5 周期的平面图形

IF 0.7 4区数学

Graphs and Combinatorics Pub Date : 2024-04-05 DOI: 10.1007/s00373-024-02773-w

Michael Savery

引用次数: 0

Walk Domination and HHD-Free Graphs 步行支配和无 HHD 图形

IF 0.7 4区数学

Graphs and Combinatorics Pub Date : 2024-04-05 DOI: 10.1007/s00373-024-02771-y

Silvia B. Tondato

引用次数: 0

Using Euler’s Formula to Find the Lower Bound of the Page Number 使用欧拉公式计算页码下限

IF 0.7 4区数学

Graphs and Combinatorics Pub Date : 2024-04-03 DOI: 10.1007/s00373-024-02775-8

Bin Zhao, Peng Li, Jixiang Meng, Yuepeng Zhang

{"title":"Using Euler’s Formula to Find the Lower Bound of the Page Number","authors":"Bin Zhao, Peng Li, Jixiang Meng, Yuepeng Zhang","doi":"10.1007/s00373-024-02775-8","DOIUrl":"https://doi.org/10.1007/s00373-024-02775-8","url":null,"abstract":"The concept of book embedding, originating in computer science, has found extensive applications in various problem domains. A book embedding of a graph G involves arranging the vertices of G in an order along a line and assigning the edges to one or more half-planes. The page number of a graph is the smallest possible number of half-planes for any book embedding of the graph. Determining the page number is a key aspect of book embedding and carries significant importance. This paper aims to investigate the non-trivial lower bound of the page number for both a graph G and a random graph (Gin mathcal {G}(n,p)) by incorporating two seemingly unrelated concepts: edge-arboricity and Euler’s Formula. Our analysis reveals that for a graph G, which is not a path, (pn(G)ge lceil frac{1}{3} a_1(G)rceil ), where (a_1(G)) denotes the edge-arboricity of G, and for an outerplanar graph, the lower bound is optimal. For (Gin mathcal {G}(n,p)), (pn(G)ge lceil frac{1}{6}np(1-o(1))rceil ) with high probability, as long as (frac{c}{n}le ple frac{root 2 of {3(n-1)}}{nlog {n}}).","PeriodicalId":12811,"journal":{"name":"Graphs and Combinatorics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140578832","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

Path Saturation Game on Six Vertices 六顶点上的路径饱和博弈

IF 0.7 4区数学

Graphs and Combinatorics Pub Date : 2024-04-03 DOI: 10.1007/s00373-024-02767-8

Paul Balister, Ali Dogan

引用次数: 0

Some Results on the Rainbow Vertex-Disconnection Colorings of Graphs 关于图的彩虹顶点-断开连接着色的一些结果

IF 0.7 4区数学

Graphs and Combinatorics Pub Date : 2024-04-02 DOI: 10.1007/s00373-024-02762-z

Yindi Weng

{"title":"Some Results on the Rainbow Vertex-Disconnection Colorings of Graphs","authors":"Yindi Weng","doi":"10.1007/s00373-024-02762-z","DOIUrl":"https://doi.org/10.1007/s00373-024-02762-z","url":null,"abstract":"Let G be a nontrivial connected and vertex-colored graph. A vertex subset X is called rainbow if any two vertices in X have distinct colors. The graph G is called rainbow vertex-disconnected if for any two vertices x and y of G, there exists a vertex subset S such that when x and y are nonadjacent, S is rainbow and x and y belong to different components of (G-S); whereas when x and y are adjacent, (S+x) or (S+y) is rainbow and x and y belong to different components of ((G-xy)-S). For a connected graph G, the rainbow vertex-disconnection number of G, rvd(G), is the minimum number of colors that are needed to make G rainbow vertex-disconnected. In this paper, we prove for any (K_4)-minor free graph, (rvd(G)le Delta (G)) and the bound is sharp. We show it is NP-complete to determine the rainbow vertex-disconnection numbers for bipartite graphs and split graphs. Moreover, we show for every (epsilon >0), it is impossible to efficiently approximate the rainbow vertex-disconnection number of any bipartite graph and split graph within a factor of (n^{frac{1}{3}-epsilon }) unless (ZPP=NP).","PeriodicalId":12811,"journal":{"name":"Graphs and Combinatorics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140578558","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

Removable Edges in Claw-Free Bricks 无爪砖的可拆卸边缘

IF 0.7 4区数学

Graphs and Combinatorics Pub Date : 2024-04-02 DOI: 10.1007/s00373-024-02769-6

引用次数: 0

Strongly Regular Graphs from Pseudocyclic Association Schemes 来自伪环关联方案的强正则图

IF 0.7 4区数学

Graphs and Combinatorics Pub Date : 2024-03-26 DOI: 10.1007/s00373-024-02764-x

Koji Momihara, Sho Suda

引用次数: 0