The List Total Colouring Conjecture is False

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--\v{S}krekovski and Hilton--Johnson from the late 1990s. ChatGPT 6 Astra Ultra discovered the counterexample with little input from the author.