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ArticleOriginal scientific text

Title

On monochromatic paths and bicolored subdigraphs in arc-colored tournaments

Authors 1, 1

Affiliations

  1. Instituto de Matemáticas, U.N.A.M. Área de la investigación científica, Circuito Exterior, Ciudad Universitaria, Coyoacán 04510, México, D.F. México

Abstract

Consider an arc-colored digraph. A set of vertices N is a kernel by monochromatic paths if all pairs of distinct vertices of N have no monochromatic directed path between them and if for every vertex v not in N there exists n ∈ N such that there is a monochromatic directed path from v to n. In this paper we prove different sufficient conditions which imply that an arc-colored tournament has a kernel by monochromatic paths. Our conditions concerns to some subdigraphs of T and its quasimonochromatic and bicolor coloration. We also prove that our conditions are not mutually implied and that they are not implied by those known previously. Besides some open problems are proposed.

Keywords

ENG
kernel, kernel by monochromatic paths, tournament

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Discussiones Mathematicae Graph Theory
2011/31/4
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Pages:
791-820
Main language of publication
English
Received
2007-09-20
Accepted
2010-12-08
Published
2011

DOI: 10.7151/dmgt.1580

Exact and natural sciences