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On monochromatic paths and bicolored subdigraphs in arc-colored tournaments

Pietra Delgado-Escalante;  Hortensia Galeana-Sánchez — 2011

Discussiones Mathematicae Graph Theory

Consider an arc-colored digraph. A set of vertices N is a kernel by monochromatic paths if all pairs of distinct vertices of N have no monochromatic directed path between them and if for every vertex v not in N there exists n ∈ N such that there is a monochromatic directed path from v to n. In this paper we prove different sufficient conditions which imply that an arc-colored tournament has a kernel by monochromatic paths. Our conditions concerns to some subdigraphs of T and its quasimonochromatic...

Kernels and cycles' subdivisions in arc-colored tournaments

Pietra Delgado-Escalante;  Hortensia Galeana-Sánchez — 2009

Discussiones Mathematicae Graph Theory

Let D be a digraph. D is said to be an m-colored digraph if the arcs of D are colored with m colors. A path P in D is called monochromatic if all of its arcs are colored alike. Let D be an m-colored digraph. A set N ⊆ V(D) is said to be a kernel by monochromatic paths of D if it satisfies the following conditions: a) for every pair of different vertices u,v ∈ N there is no monochromatic directed path between them; and b) for every vertex x ∈ V(D)-N there is a vertex n ∈ N such that there is an xn-monochromatic...

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