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Monochromatic kernel-perfectness of special classes of digraphs

Hortensia Galeana-Sánchez; Luis Alberto Jiménez Ramírez — 2007

Discussiones Mathematicae Graph Theory

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 $α_{v}, v \in V (D)$ are monochromatic kernel-perfect digraphs if and only if the composition over D of ${(α_{v})}_{v \in V (D)}$ 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, $D^{B}$ , is a monochromatic kernel-perfect digraph.

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