The list color function 
of a graph 
is the minimum number of proper
colorings permitted by a list assignment that gives each graph
vertex exactly 
available colors. If 
counts the proper colorings selecting the color
of each graph vertex from its list 
, then
 |
Giving every graph vertex the same list shows that 
,
where 
is the chromatic polynomial. The least 
for which 
is the choice number.
For every graph 
, the list color function equals its chromatic
polynomial for all sufficiently large 
. Equality for every positive
integer 
is enumerative chromatic choosability
(Allred and Mudrock 2026). For an 
-vertex tree,
.
Both counting functions multiply over connected components.
