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On the heterochromatic number of circulant digraphs

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Galeana-Sánchez H., Neumann-Lara V.

Discussiones Mathematicae Graph Theory

2004

tom 24

nr 1

73-79

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 $D_{n,s}$ be the oriented graph such that $V(D_{n,s})$ is the set of integers mod 2n+1 and $A(D_{n,s}) = {(i,j) : j-i ∈ {1,2,...,n}∖{s}}.. In this paper we prove that $hc(D_{n,s}) ≤ 5$ for n ≥ 7. The bound is tight since equality holds when s ∈ {n,[(2n+1)/3]}.

Ograniczanie wyników

1 Discussiones Mathematicae Graph Theory

1 Galeana-Sánchez H.

1 Neumann-Lara V.

1 2004

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On the heterochromatic number of circulant digraphs