Sufficient Conditions make Graphs Edge DP-Δ-Colorable

In 2018, Dvořák and Postle introduced the concept of DP-coloring which is a generalization of list coloring and recently, Bernshteyn and Kostochka used this concept to give a new coloring, called edge DP-coloring. The edge DP-chromatic number of a graph G is denoted by χ DP ′ ( G ) . Note that χ DP ′ ( G ) ≥ Δ . It is interesting to find sufficient conditions of a graph G satisfying χ DP ′ ( G ) = Δ . In this paper, we give the sufficient conditions of a graph G in terms of its maximum degree and maximum average degree satisfying χ DP ′ ( G ) = Δ . Consequences are inferred for planar graphs in terms of their maximum degree and girth. Moreover, we also prove that a planar graph G with maximum degree Δ satisfying χ DP ′ ( G ) = Δ .