# Monochromatic paths and monochromatic sets of arcs in 3-quasitransitive digraphs

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

Discussiones Mathematicae Graph Theory (2009)

- Volume: 29, Issue: 2, page 337-347
- ISSN: 2083-5892

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topHortensia Galeana-Sánchez, R. Rojas-Monroy, and B. Zavala. "Monochromatic paths and monochromatic sets of arcs in 3-quasitransitive digraphs." Discussiones Mathematicae Graph Theory 29.2 (2009): 337-347. <http://eudml.org/doc/270653>.

@article{HortensiaGaleana2009,

abstract = {We call the digraph D an m-coloured digraph if the arcs of D are coloured with m colours. 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 of N there is no monochromatic path between them and for every vertex v ∉ N there is a monochromatic path from v to N. We denote by A⁺(u) the set of arcs of D that have u as the initial vertex. We prove that if D is an m-coloured 3-quasitransitive digraph such that for every vertex u of D, A⁺(u) is monochromatic and D satisfies some colouring conditions over one subdigraph of D of order 3 and two subdigraphs of D of order 4, then D has a kernel by monochromatic paths.},

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

journal = {Discussiones Mathematicae Graph Theory},

keywords = {m-coloured digraph; 3-quasitransitive digraph; kernel by monochromatic paths; γ-cycle; quasi-monochromatic digraph; -coloured digraph; -cycle},

language = {eng},

number = {2},

pages = {337-347},

title = {Monochromatic paths and monochromatic sets of arcs in 3-quasitransitive digraphs},

url = {http://eudml.org/doc/270653},

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 3-quasitransitive digraphs

JO - Discussiones Mathematicae Graph Theory

PY - 2009

VL - 29

IS - 2

SP - 337

EP - 347

AB - We call the digraph D an m-coloured digraph if the arcs of D are coloured with m colours. 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 of N there is no monochromatic path between them and for every vertex v ∉ N there is a monochromatic path from v to N. We denote by A⁺(u) the set of arcs of D that have u as the initial vertex. We prove that if D is an m-coloured 3-quasitransitive digraph such that for every vertex u of D, A⁺(u) is monochromatic and D satisfies some colouring conditions over one subdigraph of D of order 3 and two subdigraphs of D of order 4, then D has a kernel by monochromatic paths.

LA - eng

KW - m-coloured digraph; 3-quasitransitive digraph; kernel by monochromatic paths; γ-cycle; quasi-monochromatic digraph; -coloured digraph; -cycle

UR - http://eudml.org/doc/270653

ER -

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