Abstract
DP-coloring (also known as correspondence coloring) is a generalization of list coloring, introduced by Dvořák and Postle in 2017. It is well-known that there are non-4-choosable planar graphs. Much attention has recently been put on sufficient conditions for planar graphs to be DP- 4-colorable. In particular, for each k∈{3,4,5,6}, every planar graph without k-cycles is DP-4-colorable. In this paper, we prove that every planar graph without 7-cycles and butterflies is DP-4-colorable. Our proof can be easily modified to prove other sufficient conditions that forbid clusters formed by many triangles.
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