Characterization of $(2m,m)$-Paintable Graphs

  • Thomas Mahoney
  • Jixian Meng
  • Xuding Zhu
DOI: https://doi.org/10.37236/3876
Keywords: Painting game, on-line list colouring, paint number, fractional paint number

Abstract

In this paper, we prove that for any graph $G$ and any positive integer $m$, $G$ is $(2m,m)$-paintable if and only if $G$ is 2-paintable. It was asked by Zhu in 2009 whether $k$-paintable graphs are $(km,m)$-paintable for any positive integer $m$. Our result answers this question in the affirmative for $k=2$.

Published
2015-04-29
How to Cite
Mahoney, T., Meng, J., & Zhu, X. (2015). Characterization of $(2m,m)$-Paintable Graphs. The Electronic Journal of Combinatorics, 22(2), P2.14. https://doi.org/10.37236/3876
Issue
Volume 22, Issue 2 (2015)
Article Number
P2.14