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On (k,l)-kernel perfectness of special classes of digraphs

100%

Kucharska M.

Discussiones Mathematicae Graph Theory

2005

tom 25

nr 1-2

103-119

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].

On (k,l)-kernels of special superdigraphs of Pₘ and Cₘ

63%

Kucharska M., Kwaśnik M.

Discussiones Mathematicae Graph Theory

2001

tom 21

nr 1

95-109

The concept of (k,l)-kernels of digraphs was introduced in [2]. Next, H. Galeana-Sanchez [4] proved a sufficient condition for a digraph to have a (k,l)-kernel. The result generalizes the well-known theorem of P. Duchet and it is formulated in terms of symmetric pairs of arcs. Our aim is to give necessary and sufficient conditions for digraphs without symmetric pairs of arcs to have a (k,l)-kernel. We restrict our attention to special superdigraphs of digraphs Pₘ and Cₘ.

Ograniczanie wyników

2 Discussiones Mathematicae Graph Theory

2 Kucharska M.

1 Kwaśnik M.

1 2005

1 2001

Wyniki wyszukiwania

On (k,l)-kernel perfectness of special classes of digraphs

On (k,l)-kernels of special superdigraphs of Pₘ and Cₘ