A note on the DP-chromatic number of complete bipartite graphs.

Abstract DP-coloring (also called correspondence coloring) is a generalization of list coloring recently introduced by Dvořák and Postle. Several known bounds for the list chromatic number of a graph G , χ ℓ (G) , also hold for the DP-chromatic number of G , χ D P (G). On the other hand, there are several properties of the DP-chromatic number that show that it differs with the list chromatic number. In this note we show one such property. It is well known that χ ℓ (K k , t) = k + 1 if and only if t ≥ k k. We show that χ D P (K k , t) = k + 1 if t ≥ 1 + (k k ∕ k !) (log (k !) + 1) , and we show that χ D P (K k , t) < k + 1 if t < k k ∕ k !. [ABSTRACT FROM AUTHOR]