Hadwiger's Conjecture for some graphs with independence number two

Tong Li, Guiying Yan, Qiang Zhou

Published 2023-05-10Version 1

Let $h(G)$ denote the largest $t$ such that $G$ contains $K_t$ as a minor, $\chi(G)$ the chromatic number of $G$ respectively. In 1943, Hadwiger conjectured that $h(G) \geq \chi(G)$ for any graph $G$. In this paper, we will prove Hadwiger's Conjecture holds for $H$-free graphs with independence number two, where $H$ is any one of 4 given graphs.