Graphs with girth $2\ell$ and without longer even holes are $3$-colorable
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866918133582790656 |
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| author | Chen, Rong |
| author_facet | Chen, Rong |
| contents | For a number $\ell\geq 2$, let $\mathcal{H}_{\ell}$ denote the family of graphs which have girth $2\ell$ and have no even hole with length greater than $2\ell$. Wu, Xu, and Xu conjectured that every graph in $\bigcup_{\ell\geq2}\mathcal{H}_{\ell}$ is 3-colorable. In this paper, we prove that every graph in $\mathcal{H}_{\ell}$ is 3-colorable for any integer $\ell\geq5$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_01137 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Graphs with girth $2\ell$ and without longer even holes are $3$-colorable Chen, Rong Combinatorics For a number $\ell\geq 2$, let $\mathcal{H}_{\ell}$ denote the family of graphs which have girth $2\ell$ and have no even hole with length greater than $2\ell$. Wu, Xu, and Xu conjectured that every graph in $\bigcup_{\ell\geq2}\mathcal{H}_{\ell}$ is 3-colorable. In this paper, we prove that every graph in $\mathcal{H}_{\ell}$ is 3-colorable for any integer $\ell\geq5$. |
| title | Graphs with girth $2\ell$ and without longer even holes are $3$-colorable |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2509.01137 |