Kernels by monochromatic paths and the color-class digraph

• Autorzy: Hortensia Galeana-Sánchez
• Języki publikacji: EN

Abstrakty

EN

An m-colored digraph is a digraph whose arcs are colored with m colors. A directed path is monochromatic when its arcs are colored alike.
A set S ⊆ V(D) is a kernel by monochromatic paths whenever the two following conditions hold:
1. For any x,y ∈ S, x ≠ y, there is no monochromatic directed path between them.
2. For each z ∈ (V(D)-S) there exists a zS-monochromatic directed path.
In this paper it is introduced the concept of color-class digraph to prove that if D is an m-colored strongly connected finite digraph such that:
(i) Every closed directed walk has an even number of color changes,
(ii) Every directed walk starting and ending with the same color has an even number of color changes, then D has a kernel by monochromatic paths.
This result generalizes a classical result by Sands, Sauer and Woodrow which asserts that any 2-colored digraph has a kernel by monochromatic paths, in case that the digraph D be a strongly connected digraph.

Słowa kluczowe

EN

kernel; kernel by monochromatic paths; the color-class digraph

Kategorie tematyczne

• 05C20: Directed graphs (digraphs), tournaments

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2011
• Tom: 31
• Numer: 2
• Strony: 273-281

Daty

wydano

2011

otrzymano

2009-11-24

poprawiono

2010-12-02

zaakceptowano

2011-01-27

Twórcy

autor

Hortensia Galeana-Sánchez

• Instituto de Matemáticas, Universidad Nacional Autónoma de México, Area de la Investigación Cientifica, Ciudad Universitaria, 04510, México, D.F., México

Bibliografia

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Identyfikatory

DOI

10.7151/dmgt.1544