The correspondence chromatic number 
of a finite simple
graph 
with at least one graph vertex
is the least positive integer 
such that every assignment of pairwise disjoint finite
sets of at least 
colors to its vertices, with
a matching between the color sets at the endpoints of
each edge, admits a correspondence
coloring (Dvorák and Postle 2018). It is also called the DP chromatic
number.
For such a graph with maximum vertex degree 
, this number is at most 
, since each previously colored adjacent
vertex forbids at most one color in a successive coloring.
It is at least the choice number, since ordinary
list coloring is a special case of correspondence
coloring.
