Hadwiger's Conjecture with Certain Forbidden Induced Subgraphs

Daniel Carter

Hadwiger's Conjecture with Certain Forbidden Induced Subgraphs

Combinatorics 2022-11-02 v1

Authors: Daniel Carter

Abstract

We prove that $\{\overline{K_3}, H\}$ -free graphs are not counterexamples to Hadwiger's Conjecture, where $H$ is any one of 33 graphs on seven, eight, or nine vertices, or $H=K_8$ . This improves on past results of Plummer-Stiebitz-Toft, Kriesell, and Bosse. The proofs are mostly computer-assisted.

Keywords

hadwiger conjecture graph theory

Cite

@article{arxiv.2211.00259,
  title  = {Hadwiger's Conjecture with Certain Forbidden Induced Subgraphs},
  author = {Daniel Carter},
  journal= {arXiv preprint arXiv:2211.00259},
  year   = {2022}
}

Comments

24 pages, 5 figures

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