泛环图的充分条件

arXiv - MATH - Combinatorics Pub Date : 2024-09-18 DOI:arxiv-2409.11716

Xingzhi Zhan

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引用次数: 0

摘要

如果阶数为 $s$ 的 $G$ 的任何诱导子图的大小至少为 $t，则图 $G$ 称为 $[s,t]$-图。我们证明，每个阶数至少为 $7$ 的$2$-连接的$[4,2]$-图都是泛环图。这加强了已有的结果。有一些 2 元连接的 $[4,2]$ 图不满足 Chv'{a}tal-Erd\H{o}s 条件。我们还确定了一般 $p 的 $[p+2,p]$ 图中的无三角形图。

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A sufficient condition for pancyclic graphs

A graph $G$ is called an $[s,t]$-graph if any induced subgraph of $G$ of order $s$ has size at least $t.$ We prove that every $2$-connected $[4,2]$-graph of order at least $7$ is pancyclic. This strengthens existing results. There are $2$-connected $[4,2]$-graphs which do not satisfy the Chv\'{a}tal-Erd\H{o}s condition. We also determine the triangle-free graphs among $[p+2,p]$-graphs for a general $p.$

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arXiv - MATH - Combinatorics

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