Edge DP-coloring of planar graphs without 4-cycles and specific cycles

Abstract

The topic of finding sufficient conditions on graphs for their edge list chromatic number to equal their maximum degree has received significant attention in graph theory. Recently, Bernshteyn and Kostochka proposed a generalization of edge list coloring called edge DP-coloring. This development naturally leads to the investigation of similar conditions for edge DP-coloring. In this paper, we find that a graph G has edge DP-chromatic number equal to its maximum degree if (i) G is a planar graph without 4-cycles and 5-cycles, and the maximum degree of G is at least 6; or (ii) G is a planar graph without 4-, 6-cycles, and adjacent 5-cycles, and the maximum degree of G is at least 5. Our results generalize and strengthen previous results in the literature on edge list coloring.