Geodesic
On (k,l)-kernel perfectness of special classes of digraphs
Discussiones Mathematicae. Graph Theory, Tome 25 (2005) no. 1-2, pp. 103-119.

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In the first part of this paper we give necessary and sufficient conditions for some special classes of digraphs to have a (k,l)-kernel. One of them is the duplication of a set of vertices in a digraph. This duplication come into being as the generalization of the duplication of a vertex in a graph (see [4]). Another one is the D-join of a digraph D and a sequence α of nonempty pairwise disjoint digraphs. In the second part we prove theorems, which give necessary and sufficient conditions for special digraphs presented in the first part to be (k,l)-kernel-perfect digraphs. The concept of a (k,l)-kernel-perfect digraph is the generalization of the well-know idea of a kernel perfect digraph, which was considered in [1] and [6].
Keywords: kernel, (k,l)-kernel, kernel-perfect digraph 
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Kucharska, Magdalena. On (k,l)-kernel perfectness of special classes of digraphs. Discussiones Mathematicae. Graph Theory, Tome 25 (2005) no. 1-2, pp. 103-119. http://geodesic.mathdoc.fr/item/DMGT_2005_25_1-2_a11/

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