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arXiv · 2305.05868

Hadwiger's Conjecture for some graphs with independence number two

Tong Li·Qiang Zhou
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Abstract

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

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Tong Li, Qiang Zhou. 2024-03-30. Hadwiger's Conjecture for some graphs with independence number two. https://arxiv.org/abs/2305.05868

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