Discussiones Mathematicae Graph Theory 25(1-2) (2005) 103-119
doi: 10.7151/dmgt.1265

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Magdalena Kucharska

Institute of Mathematics
Technical University of Szczecin
Piastów 48/49, 70-310 Szczecin, Poland
e-mail: mkucharska@ps.pl


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.

2000 Mathematics Subject Classification: 05C20.


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Received 28 October 2003
Revised 11 May 2004