We call the digraph D an m-coloured digraph if the arcs of D are coloured with m colours. A directed path (or a directed cycle) is called monochromatic if all of its arcs are coloured alike. A directed cycle is called quasi-monochromatic if with at most one exception all of its arcs are coloured alike. A set N ⊆ V(D) is said to be a kernel by monochromatic paths if it satisfies the following two conditions: (i) for every pair of different vertices u,v ∈ N there is no monochromatic directed path between them and (ii) for every vertex x ∈ V(D)∖N there is a vertex y ∈ N such that there is an xy-monochromatic directed path. In this paper it is proved that if D is an m-coloured bipartite tournament such that: every directed cycle of length 4 is quasi-monochromatic, every directed cycle of length 6 is monochromatic, and D has no induced particular 6-element bipartite tournament T̃₆, then D has a kernel by monochromatic paths.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1406,
author = {Hortensia Galeana-Sanchez and Roc\'\i o Rojas-Monroy},
title = {Monochromatic paths and quasi-monochromatic cycles in edge-coloured bipartite tournaments},
journal = {Discussiones Mathematicae Graph Theory},
volume = {28},
year = {2008},
pages = {285-306},
zbl = {1156.05022},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1406}
}
Hortensia Galeana-Sanchez; Rocío Rojas-Monroy. Monochromatic paths and quasi-monochromatic cycles in edge-coloured bipartite tournaments. Discussiones Mathematicae Graph Theory, Tome 28 (2008) pp. 285-306. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1406/
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