English

Generalization of some results on list coloring and DP-coloring

Combinatorics 2019-08-12 v4

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 44, 99-cycles and cycles of two lengths from {6,7,8}\{6, 7, 8\} (R. Liu, S. Loeb, M. Rolek, Y. Yin, G. Yu, Graphs and Combinatorics 35(3) (2019) 695-705), (ii) Every planar graph without ii-cycles adjacent simultaneously to jj-cycles and kk-cycles is DP-44-colorable when {i,j,k}={3,4,5}\{i, j, k\}=\{3, 4, 5\} (P. Sittitrai, K. Nakprasit, arXiv:1801.06760(2019) preprint), (iii) Every planar graph is 55-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.

Keywords

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