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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2509.20038 |
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| _version_ | 1866918147227910144 |
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| author | Liu, Feng Liu, Hongxi |
| author_facet | Liu, Feng Liu, Hongxi |
| contents | A graph $G$ is called an $[s,t]$-graph if any induced subgraph of $G$ of order $s$ has size at least $t$. In 2024, Zhan conjectured that every $2$-connected $[p + 2, p]$-graph of order at least $2p + 3$ and with minimum degree at least $p$ is pancyclic, where $p$ is an integer with $3 \leq p \leq 5$. In this paper, we confirm the conjecture for the case $p=3$, thereby taking the first step toward a complete resolution of the conjecture. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_20038 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the pancyclicity of $2$-connected $[5,3]$-graphs Liu, Feng Liu, Hongxi Combinatorics A graph $G$ is called an $[s,t]$-graph if any induced subgraph of $G$ of order $s$ has size at least $t$. In 2024, Zhan conjectured that every $2$-connected $[p + 2, p]$-graph of order at least $2p + 3$ and with minimum degree at least $p$ is pancyclic, where $p$ is an integer with $3 \leq p \leq 5$. In this paper, we confirm the conjecture for the case $p=3$, thereby taking the first step toward a complete resolution of the conjecture. |
| title | On the pancyclicity of $2$-connected $[5,3]$-graphs |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2509.20038 |