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.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1450,
author = {Hortensia Galeana-S\'anchez and R. Rojas-Monroy and B. Zavala},
title = {Monochromatic paths and monochromatic sets of arcs in 3-quasitransitive digraphs},
journal = {Discussiones Mathematicae Graph Theory},
volume = {29},
year = {2009},
pages = {337-347},
zbl = {1193.05078},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1450}
}
Hortensia Galeana-Sánchez; R. Rojas-Monroy; B. Zavala. Monochromatic paths and monochromatic sets of arcs in 3-quasitransitive digraphs. Discussiones Mathematicae Graph Theory, Tome 29 (2009) pp. 337-347. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1450/
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