# Monochromatic paths and monochromatic sets of arcs in bipartite tournaments

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

Discussiones Mathematicae Graph Theory (2009)

- Volume: 29, Issue: 2, page 349-360
- ISSN: 2083-5892

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topHortensia Galeana-Sánchez, R. Rojas-Monroy, and B. Zavala. "Monochromatic paths and monochromatic sets of arcs in bipartite tournaments." Discussiones Mathematicae Graph Theory 29.2 (2009): 349-360. <http://eudml.org/doc/270618>.

@article{HortensiaGaleana2009,

abstract = {
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).
},

author = {Hortensia Galeana-Sánchez, R. Rojas-Monroy, B. Zavala},

journal = {Discussiones Mathematicae Graph Theory},

keywords = {m-coloured bipartite tournaments; kernel by monochromatic paths; semikernel of D modulo i by monochromatic paths; -coloured bipartite tournaments; semikernel of modulo by monochromatic paths},

language = {eng},

number = {2},

pages = {349-360},

title = {Monochromatic paths and monochromatic sets of arcs in bipartite tournaments},

url = {http://eudml.org/doc/270618},

volume = {29},

year = {2009},

}

TY - JOUR

AU - Hortensia Galeana-Sánchez

AU - R. Rojas-Monroy

AU - B. Zavala

TI - Monochromatic paths and monochromatic sets of arcs in bipartite tournaments

JO - Discussiones Mathematicae Graph Theory

PY - 2009

VL - 29

IS - 2

SP - 349

EP - 360

AB -
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).

LA - eng

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

UR - http://eudml.org/doc/270618

ER -

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