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2005 | 25 | 1-2 | 103-119
Tytuł artykułu

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

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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].
Słowa kluczowe
Wydawca
Rocznik
Tom
25
Numer
1-2
Strony
103-119
Opis fizyczny
Daty
wydano
2005
otrzymano
2003-10-28
poprawiono
2004-05-11
Twórcy
  • Institute of Mathematics, Technical University of Szczecin, Piastów 48/49, 70-310 Szczecin, Poland
Bibliografia
  • [1] C. Berge and P. Duchet, Perfect graphs and kernels, Bulletin of the Institute of Mathematics Academia Sinica 16 (1988) 263-274.
  • [2] M. Blidia, P. Duchet, H. Jacob, F. Maffray and H. Meyniel, Some operations preserving the existence of kernels, Discrete Math. 205 (1999) 211-216, doi: 10.1016/S0012-365X(99)00026-6.
  • [3] M. Borowiecki and A. Szelecka, One-factorizations of the generalized Cartesian product and of the X-join of regular graphs, Discuss. Math. Graph Theory 13 (1993) 15-19.
  • [4] M. Burlet and J. Uhry, Parity graphs, Annals of Discrete Math. 21 (1984) 253-277
  • [5] R. Diestel, Graph Theory (Springer-Verlag New-York, Inc., 1997).
  • [6] P. Duchet, A sufficient condition for a digraph to be kernel-perfect, J. Graph Theory 11 (1987) 81-85, doi: 10.1002/jgt.3190110112.
  • [7] H. Galeana-Sánchez, On the existence of (k,l)-kernels in digraphs, Discrete Math. 85 (1990) 99-102, doi: 10.1016/0012-365X(90)90167-G.
  • [8] H. Galeana-Sánchez, On the existence of kernels and h-kernels in directed graphs, Discrete Math. 110 (1992) 251-255, doi: 10.1016/0012-365X(92)90713-P.
  • [9] H. Galeana-Sanchez and V. Neumann-Lara, On the dichromatic number in kernel theory, Math. Slovaca 48 (1998) 213-219.
  • [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.
  • [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.
  • [13] M. Kwaśnik, On (k,l)-kernels in graphs and their products (PhD Thesis, Technical University of Wrocław, Wrocław, 1980).
  • [14] A. Włoch and I. Włoch, On (k,l)-kernels in generalized products, Discrete Math. 164 (1997) 295-301, doi: 10.1016/S0012-365X(96)00064-7.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1265
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