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arXiv · 2605.04022

Coloring graphs with independence number two and no odd clique immersions

Henry Echeverría·Jessica McDonald
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Abstract

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 $χ(G)\leq \lceil \frac{3(t-1)}{2}\rceil$.

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Henry Echeverría, Jessica McDonald. 2026-05-05. Coloring graphs with independence number two and no odd clique immersions. https://arxiv.org/abs/2605.04022

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