Generalization of some results on list coloring and DP-coloring
Abstract
In this work, we introduce DPG-coloring using the concepts of DP-coloring and variable degeneracy to modify the proofs on the following papers: (i) DP-3-coloring of planar graphs without , -cycles and cycles of two lengths from (R. Liu, S. Loeb, M. Rolek, Y. Yin, G. Yu, Graphs and Combinatorics 35(3) (2019) 695-705), (ii) Every planar graph without -cycles adjacent simultaneously to -cycles and -cycles is DP--colorable when (P. Sittitrai, K. Nakprasit, arXiv:1801.06760(2019) preprint), (iii) Every planar graph is -choosable (C. Thomassen, J. Combin. Theory Ser. B 62 (1994) 180-181). Using this modification, we obtain more results on list coloring, DP-coloring, list-forested coloring, and variable degeneracy.
Cite
@article{arxiv.1905.09699,
title = {Generalization of some results on list coloring and DP-coloring},
author = {Keaitsuda Maneeruk Nakprasit and Kittikorn Nakprasit},
journal= {arXiv preprint arXiv:1905.09699},
year = {2019}
}
Comments
arXiv admin note: text overlap with arXiv:1807.00815