Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2605.27943 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866913166760345600 |
|---|---|
| author | Wang, Yan Wu, Rong |
| author_facet | Wang, Yan Wu, Rong |
| 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_27943 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Graphs with girth 8 and without longer even holes are 3-colorable Wang, Yan Wu, Rong Combinatorics 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. |
| title | Graphs with girth 8 and without longer even holes are 3-colorable |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2605.27943 |