Sufficient conditions on planar graphs to have a relaxed DP-$3$-colorability

Published 7 Mar 2018 in math.CO | (1803.03527v1)

Abstract: It is known that DP-coloring is a generalization of a list coloring in simple graphs and many results in list coloring can be generalized in those of DP-coloring. In this work, we introduce a relaxed DP-coloring which is a generalization if a relaxed list coloring. We also shows that every planar graph $G$ without $4$-cycles or $6$-cycles is DP-$(k,d)^{*$-colorable.} It follows immediately that $G$ is $(k,d)^{*$-choosable.}