Disproof of the Odd Hadwiger Conjecture

TL;DR

This paper disproves the longstanding odd Hadwiger conjecture by constructing graphs that lack certain odd minors yet have high chromatic numbers, challenging previous assumptions in graph theory.

Contribution

It provides a counterexample to the odd Hadwiger conjecture, demonstrating that graphs can have high chromatic number without containing specific odd minors.

Findings

Existence of graphs without $K_t$ odd minors but with chromatic number at least (3/2 - o(1))t

Disproof of the odd Hadwiger conjecture from 1993

Strong form of the conjecture is invalidated

Abstract

We prove that there exist graphs which do not contain $K_t$ as an odd minor and whose chromatic number is at least $(\frac 32-o(1))t$. This disproves, in a strong form, the odd Hadwiger conjecture of Gerards and Seymour from 1993.