Discussiones Mathematicae Graph Theory 27(3) (2007)
389-400
DOI: https://doi.org/10.7151/dmgt.1369
MONOCHROMATIC KERNEL-PERFECTNESS OF SPECIAL CLASSES OF DIGRAPHS
| Hortensia Galeana-Sánchez
Instituto de Matemáticas | Luis Alberto Jiménez Ramírez
Facultad de Ciencias |
Abstract
In this paper, we introduce the concept of monochromatic kernel-perfect digraph, and we prove the following two results:(1) If D is a digraph without monochromatic directed cycles, then D and each αv,v ∈ V(D) are monochromatic kernel-perfect digraphs if and only if the composition over D of (αv)v ∈ V(D) is a monochromatic kernel-perfect digraph.
(2) D is a monochromatic kernel-perfect digraph if and only if for any B ⊆ V(D), the duplication of D over B, DB, is a monochromatic kernel-perfect digraph.
Keywords: kernel, kernel by monochromatic paths, composition, duplication.
2000 Mathematics Subject Classification: 05C20.
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Received 17 January 2006
Revised 11 June 2007
Accepted 11 June 2007
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