Multiple DP-Coloring of Planar Graphs Without 3-Cycles and Normally Adjacent 4-Cycles

Abstract

The concept of DP-coloring of a graph is a generalization of list coloring introduced by Dvořák and Postle (J. Combin. Theory Ser. B 129, 38–54, 2018). Multiple DP-coloring of graphs, as a generalization of multiple list coloring, was first studied by Bernshteyn, Kostochka and Zhu (J. Graph Theory 93, 203–221, 2020). This paper proves that planar graphs without 3-cycles and normally adjacent 4-cycles are (7m, 2m)-DP-colorable for every integer m. As a consequence, the strong fractional choice number of any planar graph without 3-cycles and normally adjacent 4-cycles is at most 7/2.