Odd complete bipartite minors in graphs with independence number two

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 $1\le \ell <\chi (G)$. 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 $1\le \ell <\chi (G)$.