Every 3-connected {K1,3,Γ3}-free graph is Hamilton-connected

IF 0.7 3区数学 Q2 MATHEMATICS

Discrete Mathematics Pub Date : 2024-10-31 DOI:10.1016/j.disc.2024.114305

Adam Kabela, Zdeněk Ryjáček, Mária Skyvová, Petr Vrána

引用次数: 0

Abstract

We show that every 3-connected

{K_{1, 3}, Γ_{3}}

-free graph is Hamilton-connected, where

Γ_{3}

is the graph obtained by joining two vertex-disjoint triangles with a path of length 3. This resolves one of the two last open cases in the characterization of pairs of connected forbidden subgraphs implying Hamilton-connectedness. The proof is based on a new closure technique, developed in a previous paper, and on a structural analysis of small subgraphs, cycles and paths in line graphs of multigraphs. The most technical steps of the analysis are computer-assisted.

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每个无 3 连接的 {K1,3,Γ3} 图都是汉密尔顿连接的

我们证明了每一个无 3 连接的 {K1,3,Γ3} 图都是汉密尔顿连接的，其中Γ3 是用长度为 3 的路径连接两个顶点相交的三角形所得到的图。这解决了暗示汉密尔顿连接性的成对连接的禁止子图的特征描述中最后两个开放案例之一。证明基于前一篇论文中开发的一种新的闭合技术，以及对多图行图中的小子图、循环和路径的结构分析。分析的大部分技术步骤都由计算机辅助完成。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Discrete Mathematics 数学-数学

CiteScore

1.50

自引率

12.50%

发文量

424

审稿时长

6 months

期刊介绍： Discrete Mathematics provides a common forum for significant research in many areas of discrete mathematics and combinatorics. Among the fields covered by Discrete Mathematics are graph and hypergraph theory, enumeration, coding theory, block designs, the combinatorics of partially ordered sets, extremal set theory, matroid theory, algebraic combinatorics, discrete geometry, matrices, and discrete probability theory. Items in the journal include research articles (Contributions or Notes, depending on length) and survey/expository articles (Perspectives). Efforts are made to process the submission of Notes (short articles) quickly. The Perspectives section features expository articles accessible to a broad audience that cast new light or present unifying points of view on well-known or insufficiently-known topics.