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## Discussiones Mathematicae Graph Theory

2009 | 29 | 1 | 101-117
Tytuł artykułu

### Kernels and cycles' subdivisions in arc-colored tournaments

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Let D be a digraph. D is said to be an m-colored digraph if the arcs of D are colored with m colors. A path P in D is called monochromatic if all of its arcs are colored alike. Let D be an m-colored digraph. A set N ⊆ V(D) is said to be a kernel by monochromatic paths of D if it satisfies the following conditions: a) for every pair of different vertices u,v ∈ N there is no monochromatic directed path between them; and b) for every vertex x ∈ V(D)-N there is a vertex n ∈ N such that there is an xn-monochromatic directed path in D. In this paper we prove that if T is an arc-colored tournament which does not contain certain subdivisions of cycles then it possesses a kernel by monochromatic paths. These results generalize a well known sufficient condition for the existence of a kernel by monochromatic paths obtained by Shen Minggang in 1988 and another one obtained by Hahn et al. in 2004. Some open problems are proposed.
Słowa kluczowe
EN
Kategorie tematyczne
Wydawca
Czasopismo
Rocznik
Tom
Numer
Strony
101-117
Opis fizyczny
Daty
wydano
2009
otrzymano
2007-01-30
poprawiono
2008-12-03
zaakceptowano
2008-12-03
Twórcy
• Instituto de Matemáticas, U.N.A.M. Área de la investigación científica, Circuito Exterior, Ciudad Universitaria, Coyoacán 04510, México, D.F. México
• Instituto de Matemáticas, U.N.A.M. Área de la investigación científica, Circuito Exterior, Ciudad Universitaria, Coyoacán 04510, México, D.F. México
Bibliografia
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