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Kernels in monochromatic path digraphs

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Galeana-Sánchez H., Ramírez L., Mejía H.

Discussiones Mathematicae Graph Theory

2005

tom 25

nr 3

407-417

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: (i) for every pair of different vertices u,v ∈ N there is no monochromatic directed path between them and (ii) for each vertex x ∈ (V(D)-N) there is a vertex y ∈ N such that there is an xy-monochromatic directed path. In this paper is defined the monochromatic path digraph of D, MP(D), and the inner m-colouration of MP(D). Also it is proved that if D is an m-coloured digraph without monochromatic directed cycles, then the number of kernels by monochromatic paths in D is equal to the number of kernels by monochromatic paths in the inner m-colouration of MP(D). A previous result is generalized.

Ograniczanie wyników

1 Discussiones Mathematicae Graph Theory

1 Galeana-Sánchez H.

1 Mejía H.

1 Ramírez L.

1 2005

Wyniki wyszukiwania

Kernels in monochromatic path digraphs