Odd complete bipartite minors in graphs with independence number two

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