The list total coloring conjecture asserted that the list total chromatic number of every multigraph equals its total chromatic number,
 |
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. The author checked the arguments and rewrote the exposition from drafts generated by ChatGPT, which also assisted with proofreading, references, questions about the arguments, and the figures. The author assumes responsibility for correctness.
