The list color function 
of a finite simple
graph 
with at least one graph vertex, for a positive
integer 
, 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 such 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,
where 
is a positive integer, 
. Both counting functions multiply
over connected components.
