Hadwiger's Conjecture for some graphs with independence number two

Tong Li; Qiang Zhou

Hadwiger's Conjecture for some graphs with independence number two

Combinatorics 2024-04-02 v5

Authors: Tong Li , Qiang Zhou

Abstract

Let $h(G)$ denote the largest $t$ such that $G$ contains $K_t$ as a minor and $\chi(G)$ be the chromatic number of $G$ respectively. In 1943, Hadwiger conjectured that $h(G) \geq \chi(G)$ 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.

Keywords

hadwiger conjecture graph coloring graph theory

Cite

@article{arxiv.2305.05868,
  title  = {Hadwiger's Conjecture for some graphs with independence number two},
  author = {Tong Li and Qiang Zhou},
  journal= {arXiv preprint arXiv:2305.05868},
  year   = {2024}
}

Comments

11 pages, 3 figures

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