Geodesic
Monochromatic paths and monochromatic sets of arcs in bipartite tournaments
Discussiones Mathematicae. Graph Theory, Tome 29 (2009) no. 2, pp. 349-360

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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.
Keywords: m-coloured bipartite tournaments, kernel by monochromatic paths, semikernel of D modulo i by monochromatic paths 
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Galeana-Sánchez, Hortensia; Rojas-Monroy, R.; Zavala, B. Monochromatic paths and monochromatic sets of arcs in bipartite tournaments. Discussiones Mathematicae. Graph Theory, Tome 29 (2009) no. 2, pp. 349-360. http://geodesic.mathdoc.fr/item/DMGT_2009_29_2_a9/