Coloring graphs with independence number two and no odd clique immersions

TL;DR

This paper investigates the chromatic number of graphs with independence number two that do not contain a strong odd clique immersion, establishing an upper bound based on the size of the clique.

Contribution

It provides a bound on the chromatic number for graphs excluding strong odd clique immersions when the independence number is at most two.

Findings

If lpha(G) le 2 and G has no strong odd K_t-immersion, then hi(G) le eil(3(t-1)/2)

The result links the absence of strong odd clique immersions to chromatic bounds in graphs with independence number two.

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