无{K1,3,Γ3}图中的汉密尔顿连接性闭包

IF 0.7 3区数学 Q2 MATHEMATICS

Discrete Mathematics Pub Date : 2024-07-17 DOI:10.1016/j.disc.2024.114154

Adam Kabela, Zdeněk Ryjáček, Mária Skyvová, Petr Vrána

引用次数: 0

摘要

我们介绍了{K1,3,Γ3}-无图的汉密尔顿连接性的闭合技术，其中Γ3是将两个顶点相交的三角形用一条长度为3的路径连接起来得到的图。闭合技术将无爪图转化为多图的线图，同时保留其（非）汉密尔顿连接性。闭包的主要应用在随后的一篇论文中，该论文证明了每一个 3 连接的 {K1,3,Γ3} 无爪图都是汉密尔顿连接的，从而解决了暗示汉密尔顿连接性的成对连接的禁止子图的表征中最后两个开放案例之一。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

A closure for Hamilton-connectedness in {K1,3,Γ3}-free graphs

We introduce a closure technique for Hamilton-connectedness of ${K_{1, 3}, Γ_{3}}$ -free graphs, where $Γ_{3}$ is the graph obtained by joining two vertex-disjoint triangles with a path of length 3. The closure turns a claw-free graph into a line graph of a multigraph while preserving its (non)-Hamilton-connectedness. The most technical parts of the proof are computer-assisted.

The main application of the closure is given in a subsequent paper showing that every 3-connected ${K_{1, 3}, Γ_{3}}$ -free graph is Hamilton-connected, thus resolving one of the two last open cases in the characterization of pairs of connected forbidden subgraphs implying Hamilton-connectedness.

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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.