Odd complete bipartite minors in graphs with independence number two

TL;DR

This paper extends a known graph minor result to odd minors, showing that graphs with independence number two contain specific odd minors related to their chromatic number.

Contribution

It introduces the first result on odd minors in graphs with independence number two, generalizing previous minor results to the odd minor setting.

Findings

Graphs with independence number two contain specific odd minors.

Extension of minor results to odd minors.

Generalization of previous theorems to odd minor context.

Abstract

Recently, Chen and Deng have proved that every graph $G$ with independence number two contains $K_{\ell,\chi(G)- \ell}$ as a minor for each integer $\ell$ with $1\leq\ell < \chi(G)$. In this paper, we extend this result to odd minor version. That is, we prove that each graph $G$ with independence number two contains $K_{\ell,\chi(G)- \ell}$ as an odd minor for each integer $\ell$ with $1\leq\ell < \chi(G)$.