Geodesic
Kernels in monochromatic path digraphs
Discussiones Mathematicae. Graph Theory, Tome 25 (2005) no. 3, pp. 407-417.

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We call the digraph D an m-coloured digraph if its arcs are coloured with m colours. A directed path (or a directed cycle) is called monochromatic if all of its arcs are coloured alike. Let D be an m-coloured digraph. A set N ⊆ V(D) is said to be a kernel by monochromatic paths if it satisfies the following two conditions:
Keywords: kernel, line digraph, kernel by monochromatic paths, monochromatic path digraph, edge-coloured digraph 
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Galeana-Sánchez, Hortensia; Ramírez, Laura; Mejía, Hugo. Kernels in monochromatic path digraphs. Discussiones Mathematicae. Graph Theory, Tome 25 (2005) no. 3, pp. 407-417. http://geodesic.mathdoc.fr/item/DMGT_2005_25_3_a16/

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