Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 157-01. A counterexample to Hadwiger's conjecture
Manuscript map · lines 5385–5394
OpenAI@2026-10-07#rem:oai-p-157-01
Authors: OpenAI. Family 157.
Title: A counterexample to Hadwiger's conjecture.
Abstract: We disprove Hadwiger's conjecture by constructing arbitrarily large graphs whose chromatic number exceeds their Hadwiger number. The examples have independence number at most two, and even their ordinary fractional chromatic number exceeds their Hadwiger number. Thus they also disprove the fractional-coloring weakening discussed by Reed and Seymour.
This abstract is a catalogue record. It is not a verification and not a premise. It does not close O.1. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted.
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