Coloring graphs with independence number two and no odd clique immersions

Henry Echeverría; Jessica McDonald

Coloring graphs with independence number two and no odd clique immersions

Combinatorics 2026-05-06 v1

Authors: Henry Echeverría , Jessica McDonald

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 $\alpha(G)\leq 2$ and $G$ has no strong odd $K_t$ -immersion, then $\chi(G)\leq \lceil \frac{3(t-1)}{2}\rceil$ .

Keywords

graph coloring chromatic number independence number clique immersion odd immersion

Cite

@article{arxiv.2605.04022,
  title  = {Coloring graphs with independence number two and no odd clique immersions},
  author = {Henry Echeverría and Jessica McDonald},
  journal= {arXiv preprint arXiv:2605.04022},
  year   = {2026}
}

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