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The List Total Colouring Conjecture is False
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 counterex
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