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Discussiones Mathematicae Graph Theory

2005 | 25 | 3 | 407-417
Tytuł artykułu

Kernels in monochromatic path digraphs

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Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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.
Słowa kluczowe
EN
Kategorie tematyczne
Wydawca
Czasopismo
Rocznik
Tom
Numer
Strony
407-417
Opis fizyczny
Daty
wydano
2005
otrzymano
2004-08-03
poprawiono
2004-12-10
Twórcy
• Instituto de Matemáticas, UNAM, Universidad Nacional Autónoma de México, Ciudad Universitaria, 04510, México, D.F. México
• Departamento de Matemáticas, Facultad de Ciencias, Universidad Nacional Autónoma de México, Ciudad Universitaria, 04510, México, D.F. México
• Departamento de Matemáticas, Facultad de Ciencias, Universidad Nacional Autónoma de México, Ciudad Universitaria, 04510, México, D.F. México
Bibliografia
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• [5] H. Galeana-Sánchez and V. Neumann-Lara, On kernels and semikernels of digraphs, Discrete Math. 48 (1984) 67-76, doi: 10.1016/0012-365X(84)90131-6.
• [6] H. Galeana-Sánchez, L. Pastrana Ramírez and H.A. Rincón-Mejía, Semikernels, quasikernels and Grundy functions in the line digraph, SIAM J. Disc. Math. 1 (1999) 80-83.
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• [8] H. Galeana-Sánchez and Xueliang Li, Semikernels and (k,l)-kernels in digraphs, SIAM J. Discrete Math. 11 (1998) 340-346, doi: 10.1137/S0895480195291370.
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• [11] H. Galeana-Sánchez and José de Jesús García-Ruvalcaba, Kernels in the closure of coloured digraphs, Discuss. Math. Graph Theory 20 (2000) 243-254, doi: 10.7151/dmgt.1123.
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