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

Discussiones Mathematicae Graph Theory (2005)

- Volume: 25, Issue: 1-2, page 103-119
- ISSN: 2083-5892

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topMagdalena Kucharska. "On (k,l)-kernel perfectness of special classes of digraphs." Discussiones Mathematicae Graph Theory 25.1-2 (2005): 103-119. <http://eudml.org/doc/270648>.

@article{MagdalenaKucharska2005,

abstract = {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].},

author = {Magdalena Kucharska},

journal = {Discussiones Mathematicae Graph Theory},

keywords = {kernel; (k,l)-kernel; kernel-perfect digraph; kernel perfect},

language = {eng},

number = {1-2},

pages = {103-119},

title = {On (k,l)-kernel perfectness of special classes of digraphs},

url = {http://eudml.org/doc/270648},

volume = {25},

year = {2005},

}

TY - JOUR

AU - Magdalena Kucharska

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

JO - Discussiones Mathematicae Graph Theory

PY - 2005

VL - 25

IS - 1-2

SP - 103

EP - 119

AB - 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].

LA - eng

KW - kernel; (k,l)-kernel; kernel-perfect digraph; kernel perfect

UR - http://eudml.org/doc/270648

ER -

## References

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- [10] H. Jacob, Etude theórique du noyau d' un graphe (Thèse, Univesitè Pierre et Marie Curie, Paris VI, 1979).
- [11] M. Kucharska, On (k,l)-kernels of orientations of special graphs, Ars Combin. 60 (2001) 137-147. Zbl1068.05504
- [12] M. Kucharska and M. Kwaśnik, On (k,l)-kernels of special superdigraphs of Pₘ and Cₘ, Discuss. Math. Graph Theory 21 (2001) 95-109, doi: 10.7151/dmgt.1135.
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