A sufficient condition for pancyclic graphs
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866909777291902976 |
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| author | Zhan, Xingzhi |
| author_facet | Zhan, Xingzhi |
| contents | 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 Chvátal-Erdős condition. We also determine the triangle-free graphs among $[p+2,p]$-graphs for a general $p.$ |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2409_11716 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A sufficient condition for pancyclic graphs Zhan, Xingzhi Combinatorics 05C38, 05C42, 05C45, 05C75 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 Chvátal-Erdős condition. We also determine the triangle-free graphs among $[p+2,p]$-graphs for a general $p.$ |
| title | A sufficient condition for pancyclic graphs |
| topic | Combinatorics 05C38, 05C42, 05C45, 05C75 |
| url | https://arxiv.org/abs/2409.11716 |