Geodesic
Monochromatic paths and quasi-monochromatic cycles in edge-coloured bipartite tournaments
Discussiones Mathematicae. Graph Theory, Tome 28 (2008) no. 2, pp. 285-306

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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:
Keywords: kernel, kernel by monochromatic paths, bipartite tournament 
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Galeana-Sanchez, Hortensia; Rojas-Monroy, Rocío. Monochromatic paths and quasi-monochromatic cycles in edge-coloured bipartite tournaments. Discussiones Mathematicae. Graph Theory, Tome 28 (2008) no. 2, pp. 285-306. http://geodesic.mathdoc.fr/item/DMGT_2008_28_2_a5/