Hamilton cycles in tough $(2P_2 \cup P_1)$-free graphs
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866911006623531008 |
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| author | Shan, Songling Tanyel, Arthur |
| author_facet | Shan, Songling Tanyel, Arthur |
| contents | In 1973, Chvátal conjectured that there exists a constant $t_0$ such that every $t_0$-tough graph on at least three vertices is Hamiltonian. While this conjecture is still open, work has been done to confirm it for several graph classes, including all $F$-free graphs for every 5-vertex linear forest $F$ other than $P_5$ and $2P_2\cup P_1$. In this note, we show that 11-tough $(2P_2 \cup P_1)$-free graphs on at least three vertices are Hamiltonian. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_12684 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Hamilton cycles in tough $(2P_2 \cup P_1)$-free graphs Shan, Songling Tanyel, Arthur Combinatorics In 1973, Chvátal conjectured that there exists a constant $t_0$ such that every $t_0$-tough graph on at least three vertices is Hamiltonian. While this conjecture is still open, work has been done to confirm it for several graph classes, including all $F$-free graphs for every 5-vertex linear forest $F$ other than $P_5$ and $2P_2\cup P_1$. In this note, we show that 11-tough $(2P_2 \cup P_1)$-free graphs on at least three vertices are Hamiltonian. |
| title | Hamilton cycles in tough $(2P_2 \cup P_1)$-free graphs |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2506.12684 |