Gerards–Seymour odd-minor coloring conjecture

Let $G$ be a graph and let $t$ be a positive integer. An odd-minor of a graph is a graph formed from a subgraph by contracting edge cuts; odd-minors preserve the parity of cycles. Gerards–Seymour's conjecture. Every graph that does not contain $K_t$ as an odd-minor is $(t-1)$-colorable. The conjecture was disproved by Kühn, Sauermann, Steiner, and Wigderson, who constructed graphs with no $K_t$ odd-minor and chromatic number at least $(1.5-o(1))t$.