The list total chromatic number 
of a graph 
is the least positive integer 
such that, whenever each graph vertex and graph
edge is assigned a list of 
colors, 
has a total coloring in which every graph
vertex and graph edge receives a color from its
assigned list.
Noel (2026) constructed a 20-vertex simple graph 
that is cubic and satisfies
 |
This disproved the list total coloring conjecture, which asserted equality between the list total chromatic number and total chromatic number for every multigraph.
