Discussiones Mathematicae Graph Theory 31(2) (2011)
273-281
DOI: https://doi.org/10.7151/dmgt.1544
Kernels by monochromatic paths
and the color-class digraph
Hortensia Galeana-Sánchez
Instituto de Matemáticas |
Abstract
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.
|
2.
|
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)
|
(ii)
|
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.
Keywords: kernel, kernel by monochromatic paths, the color-class digraph
2010 Mathematics Subject Classification: 05C20.
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Received 24 November 2009
Revised 2 December 2010
Accepted 27 January 2011
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