Colourings with Bounded Monochromatic Components in Graphs of Given Circumference

Bojan Mohar; Bruce Reed; David R. Wood

Colourings with Bounded Monochromatic Components in Graphs of Given Circumference

Combinatorics 2018-06-21 v2

Authors: Bojan Mohar , Bruce Reed , David R. Wood

Abstract

We prove that every graph with circumference at most $k$ is $O(\log k)$ -colourable such that every monochromatic component has size at most $O(k)$ . The $O(\log k)$ bound on the number of colours is best possible, even in the setting of colourings with bounded monochromatic degree.

Keywords

graph colouring monochromatic component circumference bounded degree

Cite

@article{arxiv.1612.05674,
  title  = {Colourings with Bounded Monochromatic Components in Graphs of Given Circumference},
  author = {Bojan Mohar and Bruce Reed and David R. Wood},
  journal= {arXiv preprint arXiv:1612.05674},
  year   = {2018}
}

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