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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2605.27943 |
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Table of Contents:
- For an integer $\ell\geq 2$, let ${\cal{H}}_{\ell}$ denote the family of graphs which have girth $2\ell$ and have no even hole of length greater than $2\ell$. Wu, Xu and Xu conjectured that every graph in $\bigcup_{\ell\geq 2} {\cal{H}}_{\ell}$ is $3$-colorable. Chen showed that every graph in $\bigcup_{\ell\geq 5} {\cal{H}}_{\ell}$ is $3$-colorable. In this paper, we prove that every graph in ${\cal{H}}_4$ is $3$-colorable.