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

[摘要] 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 res

[学科分类] 离散数学和组合数学

[关键词] Painting game;on-line list colouring;paint number;fractional paint number