Even cycles in graphs avoiding longer even cycles
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866912201444425728 |
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| author | Conlon, David Mulrenin, Eion Pohoata, Cosmin |
| author_facet | Conlon, David Mulrenin, Eion Pohoata, Cosmin |
| contents | A conjecture of Verstraëte states that for any fixed $\ell < k$ there exists a positive constant $c$ such that any $C_{2k}$-free graph $G$ contains a $C_{2\ell}$-free subgraph with at least $c |E(G)|$ edges. For $\ell = 2$, this conjecture was verified by Kühn and Osthus. We show that $C_6$ and $C_{2k}$ satisfy the conjecture for all odd $k$, but observe that a recent construction of a dense $C_{10}$-free subgraph of the hypercube yields a counterexample to the conjecture for $C_8$ and $C_{10}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_13036 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Even cycles in graphs avoiding longer even cycles Conlon, David Mulrenin, Eion Pohoata, Cosmin Combinatorics 05C35, 05C38 A conjecture of Verstraëte states that for any fixed $\ell < k$ there exists a positive constant $c$ such that any $C_{2k}$-free graph $G$ contains a $C_{2\ell}$-free subgraph with at least $c |E(G)|$ edges. For $\ell = 2$, this conjecture was verified by Kühn and Osthus. We show that $C_6$ and $C_{2k}$ satisfy the conjecture for all odd $k$, but observe that a recent construction of a dense $C_{10}$-free subgraph of the hypercube yields a counterexample to the conjecture for $C_8$ and $C_{10}$. |
| title | Even cycles in graphs avoiding longer even cycles |
| topic | Combinatorics 05C35, 05C38 |
| url | https://arxiv.org/abs/2501.13036 |