A strengthening on consecutive odd cycles in graphs of given minimum degree
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866913915717287936 |
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| author | Lin, Hao Wang, Guanghui Zhou, Wenling |
| author_facet | Lin, Hao Wang, Guanghui Zhou, Wenling |
| contents | Liu and Ma [J. Combin. Theory Ser. B, 2018] conjectured that every $2$-connected non-bipartite graph with minimum degree at least $k+1$ contains $\lceil k/2\rceil $ cycles with consecutive odd lengths. In particular, they showed that this conjecture holds when $k$ is even. In this paper, we confirm this conjecture for any $k\in \mathbb N$. Moreover, we also improve some previous results about cycles of consecutive lengths. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2410_00648 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A strengthening on consecutive odd cycles in graphs of given minimum degree Lin, Hao Wang, Guanghui Zhou, Wenling Combinatorics Liu and Ma [J. Combin. Theory Ser. B, 2018] conjectured that every $2$-connected non-bipartite graph with minimum degree at least $k+1$ contains $\lceil k/2\rceil $ cycles with consecutive odd lengths. In particular, they showed that this conjecture holds when $k$ is even. In this paper, we confirm this conjecture for any $k\in \mathbb N$. Moreover, we also improve some previous results about cycles of consecutive lengths. |
| title | A strengthening on consecutive odd cycles in graphs of given minimum degree |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2410.00648 |