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arXiv · 2512.20392

Disproof of the Odd Hadwiger Conjecture

Marcus Kühn·Lisa Sauermann·Raphael Steiner·Yuval Wigderson
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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.

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Marcus Kühn, Lisa Sauermann, Raphael Steiner, Yuval Wigderson. 2025-12-23. Disproof of the Odd Hadwiger Conjecture. https://arxiv.org/abs/2512.20392

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