k-kernels in generalizations of transitive digraphs
Discussiones Mathematicae. Graph Theory, Tome 31 (2011) no. 2, pp. 293-312.

Voir la notice de l'article provenant de la source Library of Science

Let D be a digraph, V(D) and A(D) will denote the sets of vertices and arcs of D, respectively.
Keywords: digraph, kernel, (k,l)-kernel, k-kernel, transitive digraph, quasi-transitive digraph, right-pretransitive digraph, left-pretransitive digraph, pretransitive digraph
@article{DMGT_2011_31_2_a6,
     author = {Galeana-S\'anchez, Hortensia and Hern\'andez-Cruz, C\'esar},
     title = {k-kernels in generalizations of transitive digraphs},
     journal = {Discussiones Mathematicae. Graph Theory},
     pages = {293--312},
     publisher = {mathdoc},
     volume = {31},
     number = {2},
     year = {2011},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DMGT_2011_31_2_a6/}
}
TY  - JOUR
AU  - Galeana-Sánchez, Hortensia
AU  - Hernández-Cruz, César
TI  - k-kernels in generalizations of transitive digraphs
JO  - Discussiones Mathematicae. Graph Theory
PY  - 2011
SP  - 293
EP  - 312
VL  - 31
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DMGT_2011_31_2_a6/
LA  - en
ID  - DMGT_2011_31_2_a6
ER  - 
%0 Journal Article
%A Galeana-Sánchez, Hortensia
%A Hernández-Cruz, César
%T k-kernels in generalizations of transitive digraphs
%J Discussiones Mathematicae. Graph Theory
%D 2011
%P 293-312
%V 31
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DMGT_2011_31_2_a6/
%G en
%F DMGT_2011_31_2_a6
Galeana-Sánchez, Hortensia; Hernández-Cruz, César. k-kernels in generalizations of transitive digraphs. Discussiones Mathematicae. Graph Theory, Tome 31 (2011) no. 2, pp. 293-312. http://geodesic.mathdoc.fr/item/DMGT_2011_31_2_a6/

[1] J. Bang-Jensen and G. Gutin, Digraphs. Theory, Algorithms and Applications (Springer-Verlag Berlin Heidelberg New York, 2002).

[2] J. Bang-Jensen and J. Huang, Quasi-transitive digraphs, J. Graph Theory 20 (1995) 141-161, doi: 10.1002/jgt.3190200205.

[3] J. Bang-Jensen and J. Huang, Kings in quasi-transitive digraphs, Discrete Math. 185 (1998) 19-27, doi: 10.1016/S0012-365X(97)00179-9.

[4] C. Berge, Graphs (North-Holland, Amsterdam New York, 1985).

[5] C. Berge, Some classes of perfect graphs, in: Graph Theory and Theoretical Physics (Academic Press, London, 1967) 155-165, MR 38 No. 1017.

[6] C. Berge and P. Duchet, Recent problems and results about kernels in directed graphs, Discrete Math. 86 (1990) 27-31, doi: 10.1016/0012-365X(90)90346-J.

[7] E. Boros and V. Gurvich, Perfect graphs are kernel solvable, Discrete Math. 159 (1996) 35-55, doi: 10.1016/0012-365X(95)00096-F.

[8] M. Chudnovsky, N. Robertson, P. Seymour and R. Thomas, The Strong Perfect Graph Theorem, Annals of Math. 164 (2006) 51-229.

[9] R. Diestel, Graph Theory 3rd Edition (Springer-Verlag Berlin Heidelberg New York, 2005).

[10] P. Duchet, Graphes Noyau-Parfaits, Annals of Discrete Math. 9 (1980) 93-101, doi: 10.1016/S0167-5060(08)70041-4.

[11] 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.

[12] H. Galeana-Sánchez and R. Rojas-Monroy, Kernels in quasi-transitive digraphs, Discrete Math. 306 (2006) 1969-1974, doi: 10.1016/j.disc.2006.02.015.

[13] A. Ghouila-Houri, Caractérization des graphes non orientés dont on peut orienter les arretes de maniere a obtenir le graphe dune relation dordre, Comptes Rendus de l'Académie des Sciences Paris 254 (1962) 1370-1371.

[14] I. Golfeder, (k,l)-kernels in quasi-transitive digraphs, Instituto de Matemáticas de la Universidad Nacional Autónoma de México, Publicación preliminar 866 (2009).

[15] 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.

[16] M. Kwaśnik, On (k,l)-kernels on Graphs and Their Products, Doctoral dissertation (Technical University of Wrocław, Wrocław, 1980).

[17] M. Kwaśnik, The Generalizaton of Richardson's Theorem, Discuss. Math. 4 (1981) 11-14.

[18] V. Neumann-Lara, Semin'ucleos de una digráfica, Anales del Instituto de Matemáticas II (1971).

[19] M. Richardson, On Weakly Ordered Systems, Bull. Amer. Math. Soc. 52 (1946) 113-116, doi: 10.1090/S0002-9904-1946-08518-3.

[20] W. Szumny, A. Włoch and I. Włoch, On (k,l)-kernels in D-join of digraphs, Discuss. Math. Graph Theory 27 (2007) 457-470, doi: 10.7151/dmgt.1373.

[21] W. Szumny, A. Włoch and I. Włoch, On the existence and on the number of (k,l)-kernels in the lexicographic product of graphs, Discrete Math. 308 (2008) 4616-4624, doi: 10.1016/j.disc.2007.08.078.

[22] J. Von Neumann and O. Morgenstern, Theory of Games and Economic Behavior (Princeton University Press, Princeton, 1953).

[23] A. Włoch and I. Włoch, On (k,l)-kernels in generalized products, Discrete Math. 164 (1997) 295-301.