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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2406.17631 |
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| _version_ | 1866911932335783936 |
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| author | Guan, Xiaxia Ma, Hongxia Wang, Maoqun |
| author_facet | Guan, Xiaxia Ma, Hongxia Wang, Maoqun |
| contents | A spannning subgraph $F$ of $G$ is a $\{K_2,C_n\}$-factor if each component of $F$ is either $K_{2}$ or $C_{n}$. A graph $G$ is called a $(\{K_2,C_n\},n)$-factor critical avoidable graph if $G-X-e$ has a $\{K_2,C_n\}$-factor for any $S\subseteq V(G)$ with $|X|=n$ and $e\in E(G-X)$. In this paper, we first obtain a sufficient condition with regard to isolated toughness of a graph $G$ such that $G$ is $\{K_2,C_{n}\}$-factor critical avoidable. In addition, we give a sufficient condition with regard to tight toughness and isolated toughness of a graph $G$ such that $G$ is $\{K_2,C_{2i+1}|i \geqslant 2\}$-factor critical avoidable respectively. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_17631 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Tight Toughness and Isolated Toughness for $\{K_2,C_n\}$-factor critical avoidable graph Guan, Xiaxia Ma, Hongxia Wang, Maoqun Combinatorics A spannning subgraph $F$ of $G$ is a $\{K_2,C_n\}$-factor if each component of $F$ is either $K_{2}$ or $C_{n}$. A graph $G$ is called a $(\{K_2,C_n\},n)$-factor critical avoidable graph if $G-X-e$ has a $\{K_2,C_n\}$-factor for any $S\subseteq V(G)$ with $|X|=n$ and $e\in E(G-X)$. In this paper, we first obtain a sufficient condition with regard to isolated toughness of a graph $G$ such that $G$ is $\{K_2,C_{n}\}$-factor critical avoidable. In addition, we give a sufficient condition with regard to tight toughness and isolated toughness of a graph $G$ such that $G$ is $\{K_2,C_{2i+1}|i \geqslant 2\}$-factor critical avoidable respectively. |
| title | Tight Toughness and Isolated Toughness for $\{K_2,C_n\}$-factor critical avoidable graph |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2406.17631 |