k-tuple chromatic number of the cartesian product of graphs

Abstract : 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(GH) = max{χ(G), χ(H)}. In this paper, we show that there exist graphs G and H such that χ k (GH) > max{χ k (G), χ k (H)} for k ≥ 2. Moreover, we also show that there exist graph families such 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.
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Submitted on : Wednesday, January 14, 2015 - 9:24:38 PM
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  • HAL Id : hal-01103534, version 1


Flavia Bonomo, Ivo Koch, Pablo Torres, Mario Valencia-Pabon. k-tuple chromatic number of the cartesian product of graphs. 2014. ⟨hal-01103534⟩



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