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Disproof of the Odd Hadwiger Conjecture

Combinatorics 2025-12-24 v1

Abstract

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

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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}
}

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24 pages