- Tytuł:
- Kernels in edge coloured line digraph
- Autorzy:
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Galeana-Sánchez, H.
Pastrana Ramírez, L. - Powiązania:
- https://bibliotekanauki.pl/articles/744205.pdf
- Data publikacji:
- 1998
- Wydawca:
- Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
- Tematy:
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kernel
kernel by monochromatic paths
line digraph
edge coloured digraph - Opis:
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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). - Źródło:
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Discussiones Mathematicae Graph Theory; 1998, 18, 1; 91-98
2083-5892 - Pojawia się w:
- Discussiones Mathematicae Graph Theory
- Dostawca treści:
- Biblioteka Nauki
Artykuł