On the heterochromatic number of circulant digraphs
Hortensia Galeana-Sánchez, Víctor Neumann-Lara (2004)
Discussiones Mathematicae Graph Theory
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The heterochromatic number hc(D) of a digraph D, is the minimum integer k such that for every partition of V(D) into k classes, there is a cyclic triangle whose three vertices belong to different classes. For any two integers s and n with 1 ≤ s ≤ n, let be the oriented graph such that is the set of integers mod 2n+1 and In this paper we prove that for n ≥ 7. The bound is tight since equality holds when s ∈ n,[(2n+1)/3].