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Kernels in edge coloured line digraph

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Galeana-Sánchez H., Pastrana Ramírez L.

Discussiones Mathematicae Graph Theory

1998

tom 18

nr 1

91-98

We call the digraph D an m-coloured digraph if the arcs of D 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) is said to be a kernel by monochromatic paths if it satisfies the two following conditions (i) for every pair of different vertices u, v ∈ N there is no monochromatic directed path between them and (ii) for every vertex x ∈ V(D)-N there is a vertex y ∈ N such that there is an xy-monochromatic directed path. Let D be an m-coloured digraph and L(D) its line digraph. The inner m-coloration of L(D) is the edge coloration of L(D) defined as follows: If h is an arc of D of colour c, then any arc of the form (x,h) in L(D) also has colour c. In this paper 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 edge coloration of L(D).

Ograniczanie wyników

1 Discussiones Mathematicae Graph Theory

1 Galeana-Sánchez H.

1 Pastrana Ramírez L.

1 1998

Wyniki wyszukiwania

Kernels in edge coloured line digraph