Disproof of the Odd Hadwiger Conjecture
Combinatorics
2025-12-24 v1
Abstract
We prove that there exist graphs which do not contain as an odd minor and whose chromatic number is at least . This disproves, in a strong form, the odd Hadwiger conjecture of Gerards and Seymour from 1993.
Cite
@article{arxiv.2512.20392,
title = {Disproof of the Odd Hadwiger Conjecture},
author = {Marcus Kühn and Lisa Sauermann and Raphael Steiner and Yuval Wigderson},
journal= {arXiv preprint arXiv:2512.20392},
year = {2025}
}
Comments
24 pages