On $2$-factors of Hamiltonian graphs
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866913115372781568 |
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| author | Díaz, Alberto Espuny Girão, António Granet, Bertille Kronenberg, Gal |
| author_facet | Díaz, Alberto Espuny Girão, António Granet, Bertille Kronenberg, Gal |
| contents | Let $k\geq 2$. We show that, for a sufficiently small $\varepsilon>0$, any sufficiently large $n$-vertex Hamiltonian graph of minimum degree at least $n^{1-\varepsilon}$ contains a $2$-factor consisting of exactly $k$ cycles. This is the first minimum-degree condition which is polynomially smaller than linear. Our methods yield an analogous result when the host graph is not required to contain a Hamilton cycle, but only a $2$-factor consisting of at most $k$ cycles; this answers a question of Bucić, Jahn, Pokrovskiy and Sudakov. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_11288 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On $2$-factors of Hamiltonian graphs Díaz, Alberto Espuny Girão, António Granet, Bertille Kronenberg, Gal Combinatorics Let $k\geq 2$. We show that, for a sufficiently small $\varepsilon>0$, any sufficiently large $n$-vertex Hamiltonian graph of minimum degree at least $n^{1-\varepsilon}$ contains a $2$-factor consisting of exactly $k$ cycles. This is the first minimum-degree condition which is polynomially smaller than linear. Our methods yield an analogous result when the host graph is not required to contain a Hamilton cycle, but only a $2$-factor consisting of at most $k$ cycles; this answers a question of Bucić, Jahn, Pokrovskiy and Sudakov. |
| title | On $2$-factors of Hamiltonian graphs |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2605.11288 |