Defective 2-colorings of planar graphs without 4-cycles and 5-cycles

Pongpat Sittitrai; Kittikorn Nakprasit

Defective 2-colorings of planar graphs without 4-cycles and 5-cycles

Combinatorics 2016-12-01 v1

Authors: Pongpat Sittitrai , Kittikorn Nakprasit

Abstract

Let $G$ be a graph without 4-cycles and 5-cycles. We show that the problem to determine whether $G$ is $(0,k)$ -colorable is NP-complete for each positive integer $k.$ Moreover, we construct non- $(1,k)$ -colorable planar graphs without 4-cycles and 5-cycles for each positive integer $k.$ Finally, we prove that $G$ is $(d_1,d_2)$ -colorable where $(d_1,d_2)=(4,4), (3,5),$ and $(2,9).$

Keywords

defective coloring planar graphs 4-cycles 5-cycles NP-complete (d1,d2)-colorable

Cite

@article{arxiv.1611.10239,
  title  = {Defective 2-colorings of planar graphs without 4-cycles and 5-cycles},
  author = {Pongpat Sittitrai and Kittikorn Nakprasit},
  journal= {arXiv preprint arXiv:1611.10239},
  year   = {2016}
}

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