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arXiv · 2609.38417

The List Total Colouring Conjecture is False

Jonathan A. Noel
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Abstract

We exhibit a cubic graph with total chromatic number equal to four and list total chromatic number five. This disproves the List Total Colouring Conjecture of Borodin--Kostochka--Woodall, Juvan--Mohar--Škrekovski and Hilton--Johnson from the late 1990s. ChatGPT 6 Astra Ultra discovered the counterexample with little input from the author.

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Jonathan A. Noel. 2026-10-09. The List Total Colouring Conjecture is False. https://arxiv.org/abs/2609.38417

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