Woodall–Seymour bipartite minor conjecture

Let $G$ be a finite simple graph, and let $\chi(G)$ denote its chromatic number. For positive integers $\ell$ with $\ell<\chi(G)$, let $K_{\ell,\chi(G)-\ell}$ be the complete bipartite graph with parts of those sizes. Woodall–Seymour's conjecture. Every graph $G$ contains $K_{\ell,\chi(G)-\ell}$ as a minor for any positive integer $\ell$ with $\ell<\chi(G)$. This is a weakening of Hadwiger's conjecture; the source presents it as a proposed variant, without stating its resolution.