Coloring graphs with independence number two and no odd clique immersions
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866909014744367104 |
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| author | Echeverría, Henry McDonald, Jessica |
| author_facet | Echeverría, Henry McDonald, Jessica |
| contents | We study the chromatic number of graphs that exclude a clique as a strong odd immersion and have independence number two. Given a graph $G$ and $t\in\mathbb{Z}^+$, we prove that if $α(G)\leq 2$ and $G$ has no strong odd $K_t$-immersion, then $χ(G)\leq \lceil \frac{3(t-1)}{2}\rceil$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_04022 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Coloring graphs with independence number two and no odd clique immersions Echeverría, Henry McDonald, Jessica Combinatorics We study the chromatic number of graphs that exclude a clique as a strong odd immersion and have independence number two. Given a graph $G$ and $t\in\mathbb{Z}^+$, we prove that if $α(G)\leq 2$ and $G$ has no strong odd $K_t$-immersion, then $χ(G)\leq \lceil \frac{3(t-1)}{2}\rceil$. |
| title | Coloring graphs with independence number two and no odd clique immersions |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2605.04022 |