Monochromatic paths and monochromatic sets of arcs in bipartite tournaments
Hortensia Galeana‐Sánchez, Rocı́o Rojas-Monroy, B. Zavala · Discussiones Mathematicae Graph Theory · 2009
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.In this paper we introduce the concept of semikernel modulo i by monochromatic paths of an m-coloured digraph.This concept allow us to find sufficient conditions for the existence of a kernel by monochromatic paths in an m-coloured digraph.In particular we deal with bipartite tournaments such that A + (z) is monochromatic for each z ∈ V (D).