Choosability and paintability of the lexicographic product of graphs
Balázs Keszegh, Xuding Zhu · arXiv (Cornell University) · 2015
This paper studies the choice number and paint number of the lexicographic product of graphs. We prove that if $G$ has maximum degree $Δ$, then for any graph $H$ on $n$ vertices $ch(G[H]) \le (4Δ+2)(ch(H) +\log_2 n)$ and $χ_P(G[H]) \le (4Δ+2) (χ_P(H)+ \log_2 n)$.