Vertex partitions of $(C_3,C_4,C_6)$-free planar graphs

François Dross; Pascal Ochem

Vertex partitions of $(C_3,C_4,C_6)$-free planar graphs

Discrete Mathematics 2017-11-27 v1 Combinatorics

Authors: François Dross , Pascal Ochem

Abstract

A graph is $(k_1,k_2)$ -colorable if its vertex set can be partitioned into a graph with maximum degree at most $k_1$ and and a graph with maximum degree at most $k_2$ . We show that every $(C_3,C_4,C_6)$ -free planar graph is $(0,6)$ -colorable. We also show that deciding whether a $(C_3,C_4,C_6)$ -free planar graph is $(0,3)$ -colorable is NP-complete.

Keywords

vertex partition planar graphs c3 c4 c6-free graph coloring np-complete degree constraint

Cite

@article{arxiv.1711.08710,
  title  = {Vertex partitions of $(C_3,C_4,C_6)$-free planar graphs},
  author = {François Dross and Pascal Ochem},
  journal= {arXiv preprint arXiv:1711.08710},
  year   = {2017}
}

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