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arXiv:2609.38417math.CO

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.

arXiv comments
6 pages, 2 figures
Journal reference
DOI
Subjects
math.COCombinatorics

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