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].
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1265,
author = {Magdalena Kucharska},
title = {On (k,l)-kernel perfectness of special classes of digraphs},
journal = {Discussiones Mathematicae Graph Theory},
volume = {25},
year = {2005},
pages = {103-119},
zbl = {1074.05043},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1265}
}
Magdalena Kucharska. On (k,l)-kernel perfectness of special classes of digraphs. Discussiones Mathematicae Graph Theory, Tome 25 (2005) pp. 103-119. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1265/
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