DMGT

ISSN 1234-3099 (print version)

ISSN 2083-5892 (electronic version)

https://doi.org/10.7151/dmgt

Discussiones Mathematicae Graph Theory

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Discussiones Mathematicae Graph Theory

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Discussiones Mathematicae Graph Theory 21(1) (2001) 95-109
DOI: 10.7151/dmgt.1135

ON (k,l)-KERNELS OF SPECIAL SUPERDIGRAPHS
OF Pm AND Cm

Magdalena Kucharska and Maria Kwaśnik

Institute of Mathematics
Technical University of Szczecin
ul. Piastów 48/49, 70-310 Szczecin

e-mail: magdakucharska@poczta.wp.pl
e-mail: kwasnik@arcadia.tuniv.szczecin.pl

Abstract

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.

Keywords: kernel, semikernel, (k,l)-kernel.

2000 Mathematics Subject Classification: 05C20.

References

[1] C. Berge, Graphs and Hypergraphs (North-Holland, Amsterdam, 1976).
[2] M. Kwaśnik, The generalization of Richardson theorem, Discuss. Math. IV (1981) 11-14.
[3] V. Neumann-Lara, Seminúcleas en una digráfica, Anales del Instituto de Matemáticas de la Universidad Nacional Autónoma de México 11 (1971) 55-62.
[4] 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.
[5] I. Włoch, Minimal Hamiltonian graphs having a strong (k,k−2)-kei>, Zeszyty Naukowe Politechniki Rzeszowskiej No. 127 (1994) 93-98.

Received 27 September 2000