Monochromatic paths and monochromatic sets of arcs in bipartite tournaments

• Autorzy: Hortensia Galeana-Sánchez , R. Rojas-Monroy , B. Zavala
• Języki publikacji: EN

Abstrakty

EN

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).

Słowa kluczowe

EN

m-coloured bipartite tournaments; kernel by monochromatic paths; semikernel of D modulo i by monochromatic paths

Kategorie tematyczne

• 05C15: Coloring of graphs and hypergraphs
• 05C20: Directed graphs (digraphs), tournaments

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2009
• Tom: 29
• Numer: 2
• Strony: 349-360

Daty

wydano

2009

otrzymano

2007-11-06

poprawiono

2009-03-20

zaakceptowano

2009-03-20

Twórcy

autor

Hortensia Galeana-Sánchez

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

autor

R. Rojas-Monroy

• Facultad de Ciencias, Universidad Autónoma del Estado de México, Instituto Literario, Centro 50000, Toluca, Edo. de México, México

autor

B. Zavala

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

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Identyfikatory

DOI

10.7151/dmgt.1451