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arXiv · 2609.23291

The Partial List Colouring Conjecture is False

Jonathan A. Noel
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Abstract

We exhibit a graph $G$ with $14$ vertices and list chromatic number equal to $3$ such that there is a $2$-list assignment $L$ of $G$ such that at most $9$ vertices of $G$ can be properly coloured from $L$. This disproves the Partial List Colouring Conjecture of Albertson, Grossman and Haas. This counterexample was discovered and fully verified by ChatGPT 6 Astra Ultra after some persistent prompting, but almost no mathematical input, from the author.

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Jonathan A. Noel. 2026-09-20. The Partial List Colouring Conjecture is False. https://arxiv.org/abs/2609.23291

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