Extensions of edge-coloured digraphs
نویسنده
چکیده
A digraph D is said to be 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. A set N ⊆ V (D) of vertices of D is said to be a kernel by monochromatic paths of the m-coloured digraph D, if it satisfies the two following properties : (1) N is independent by monochromatic paths; i.e. for any two different vertices x, y ∈ N , there is no monochromatic directed path between them, and (2) N is absorbent by monochromatic paths; i.e. for each vertex u ∈ V (D)−N , there exists a uv-monochromatic directed path, for some v ∈ N . In this paper we present a method to construct a large variety of m-coloured digraphs with (resp. without a kernel) kernel by monochromatic paths; starting with a given m-coloured digraph D0. A previous result is generalized. Key–Words: kernel, kernel by monochromatic paths, m-coloured digraph 2000 Mathematic Subject Classification: 05C20
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