Monochromatic paths and monochromatic sets of arcs in bipartite tournaments

Hortensia Galeana-Sánchez ; R. Rojas-Monroy ; B. Zavala

Discussiones Mathematicae Graph Theory, Tome 29 (2009), p. 349-360 / Harvested from The Polish Digital Mathematics Library

Résumé

We call the digraph D an m-coloured digraph if the arcs of D are coloured with m colours and all of them are used. A directed path is called monochromatic if all of its arcs are coloured alike. A set N of vertices of D is called a kernel by monochromatic paths if for every pair of vertices there is no monochromatic path between them and for every vertex v in V(D)∖N there is a monochromatic path from v to some vertex in N. We denote by A⁺(u) the set of arcs of D that have u as the initial endpoint. In this paper we introduce the concept of semikernel modulo i by monochromatic paths of an m-coloured digraph. This concept allow us to find sufficient conditions for the existence of a kernel by monochromatic paths in an m-coloured digraph. In particular we deal with bipartite tournaments such that A⁺(z) is monochromatic for each z ∈ V(D).

Détail

Publié le : 2009-01-01

Zbl 1194.05038

EUDML-ID : urn:eudml:doc:270618

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