The choice number, or list chromatic number, of a graph 
is the least integer 
such that for every assignment of a list
of 
colors to each graph
vertex, the vertices can be properly
colored by choosing the color of each graph vertex
from its list.
The partial list coloring conjecture asserted that if a graph 
on 
vertices has choice number
, then every assignment of lists of size
permits a proper
coloring of at least 
vertices. Noel (2026) disproved the conjecture
by constructing a 14-vertex graph of choice number 3 with
a 2-list assignment from which at most 9 vertices
can be properly colored.
Noel (2026) reports that ChatGPT 6 Astra Ultra discovered and fully verified the counterexample, subsequently found the human-checkable proof, and generated the initial draft after persistent prompting but almost no mathematical input from the author. The author fully checked the arguments and assumes responsibility for their correctness.
Gu and Xu (2026) proved that graphs having no complete graph 
as a graph minor have choice number 
. For such a graph on 
vertices,
they also obtained the bound 
for 
, where 
denotes big-O notation and
is the natural
logarithm. Gu and Xu (2026) credit ChatGPT with discovering a key proposition
and report using it for parameter choices, proof revisions, and exposition. The authors
checked the arguments and take responsibility for them.
-Minor-Free Graphs." 1 Oct 2026.