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2011 | 31 | 2 | 273-281
Tytuł artykułu

Kernels by monochromatic paths and the color-class digraph

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