{"id":"openai-math/A-counterexample-to-the-Colin-de-Verdiere-chromatic-conjecture","pdf":"https://github.com/openai/math/blob/main/preprints/A-counterexample-to-the-Colin-de-Verdiere-chromatic-conjecture-September-23-2026/paper.pdf","url":"https://github.com/openai/math/tree/main/preprints/A-counterexample-to-the-Colin-de-Verdiere-chromatic-conjecture-September-23-2026","tags":["graph-coloring","spectral-graph-theory","chromatic-number","extremal-graph-theory"],"score":0,"title":"A counterexample to the Colin de Verdière chromatic conjecture","domain":"Combinatorics","family":"157","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.CO","summary":"We disprove the Colin de Verdière chromatic conjecture by constructing graphs whose chromatic number exceeds their Colin de Verdière invariant by more than one. The examples have independence number at most two. In fact, their ordinary fractional chromatic number also exceeds their Colin de Verdière invariant by more than one.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-09-23","reactions":{},"formalized":false,"family_title":"Graph coloring, clique minors, and Colin de Verdière invariants"}