DP-coloring on planar graphs without given adjacent short cycles
Danjun Huang, Jingran Qi · Discrete Mathematics Algorithms and Applications · 2020
DP-coloring (also known as correspondence coloring) introduced by Dvor̆ák and Postle (2015) is a generalization of list coloring. In 2019, Chen et al. showed that planar graphs without [Formula: see text]-cycles adjacent to [Formula: see text]-cycles are DP-[Formula: see text]-colorable for [Formula: see text] and [Formula: see text]. In this paper, we will prove that planar graphs without [Formula: see text]-cycles adjacent simultaneously to [Formula: see text]-cycles and [Formula: see text]-cycles are DP-[Formula: see text]-colorable, which is an extension of the above result.