Degree sequence condition for Hamiltonicity in tough graphs
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866908723089244160 |
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| author | Shan, Songling Tanyel, Arthur |
| author_facet | Shan, Songling Tanyel, Arthur |
| contents | Generalizing both Dirac's condition and Ore's condition for Hamilton cycles, Chvátal in 1972 established a degree sequence condition for the existence of a Hamilton cycle in a graph. Hoàng in 1995 generalized Chvátal's degree sequence condition for 1-tough graphs and conjectured a $t$-tough analogue for any positive integer $t\ge 1$. Hoàng in the same paper verified his conjecture for $t\le 3$ and recently Hoàng and Robin verified the conjecture for $t=4$. In this paper, we confirm the conjecture for all $t\ge 4$. The proof depends on two newly established results on cycle structures in tough graphs, which hold independent interest. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_04728 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Degree sequence condition for Hamiltonicity in tough graphs Shan, Songling Tanyel, Arthur Combinatorics Generalizing both Dirac's condition and Ore's condition for Hamilton cycles, Chvátal in 1972 established a degree sequence condition for the existence of a Hamilton cycle in a graph. Hoàng in 1995 generalized Chvátal's degree sequence condition for 1-tough graphs and conjectured a $t$-tough analogue for any positive integer $t\ge 1$. Hoàng in the same paper verified his conjecture for $t\le 3$ and recently Hoàng and Robin verified the conjecture for $t=4$. In this paper, we confirm the conjecture for all $t\ge 4$. The proof depends on two newly established results on cycle structures in tough graphs, which hold independent interest. |
| title | Degree sequence condition for Hamiltonicity in tough graphs |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2405.04728 |