k-tuple colorings of the Cartesian product of graphs

Flavia Bonomo, Ivo Koch, Pablo Torres, Mario Valencia-Pabon
2018 Discrete Applied Mathematics  
A k-tuple coloring of a graph G assigns a set of k colors to each vertex of G such that if two vertices are adjacent, the corresponding sets of colors are disjoint. The k-tuple chromatic number of G, χ k (G), is the smallest t so that there is a k-tuple coloring of G using t colors. It is well known that χ(G H) = max{χ(G), χ(H)}. In this paper, we show that there exist graphs G and H such that χ k (G H) > max{χ k (G), χ k (H)} for k ≥ 2. Moreover, we also show that there exist graph families
more » ... h that, for any k ≥ 1, the k-tuple chromatic number of their cartesian product is equal to the maximum k-tuple chromatic number of its factors.
doi:10.1016/j.dam.2017.02.003 fatcat:wfaxm5xtcbfabntsvjm6mmlxry