The list total coloring conjecture asserted that the list total chromatic number of every multigraph equals its total chromatic number,
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Noel (2026) disproved the conjecture by constructing a 20-vertex simple graph 
that is cubic and has 
but 
. The graph consists
of four vertex-disjoint copies of 
, with their twelve degree-two
vertices paired by six additional edges,
one joining each pair of copies.
Noel (2026) reports that ChatGPT 6 Astra Ultra produced the counterexample after being prompted to disprove the conjecture. ChatGPT also assisted with questions about the arguments. The author checked the arguments. The author assumes responsibility for correctness.
