ISSN 1234-3099 (print version)

ISSN 2083-5892 (electronic version)

Discussiones Mathematicae Graph Theory

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Discussiones Mathematicae Graph Theory


Discussiones Mathematicae Graph Theory 24(1) (2004) 73-79
DOI: 10.7151/dmgt.1214


Hortensia Galeana-Sánchez and Víctor Neumann-Lara

Instituto de Matemáticas, UNAM
Universidad Nacional Autónoma de México
Ciudad Universitaria
04510, México, D.F., MÉXICO


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 Dn,s be the oriented graph such that V(Dn,s) is the set of integers mod 2n+1 and A(Dn,s) = {(i,j) : j− i ∈ {1,2,...,n}∖{s}}.

In this paper we prove that hc(Dn,s) ≤ 5 for n ≥ 7. The bound is tight since equality holds when s ∈ {n,[(2n+1)/3]}.

Keywords: circulant tournament, vertex colouring, heterochromatic number, heterochromatic triangle.

2000 Mathematic Subject Classification: 05C20, 05C15.


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Received 29 June 2001
Revised 13 May 2003