Geodesic
On (k,l)-kernels of special superdigraphs of Pₘ and Cₘ
Discussiones Mathematicae. Graph Theory, Tome 21 (2001) no. 1, pp. 95-109.

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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 
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Kucharska, Magdalena; Kwaśnik, Maria. On (k,l)-kernels of special superdigraphs of Pₘ and Cₘ. Discussiones Mathematicae. Graph Theory, Tome 21 (2001) no. 1, pp. 95-109. http://geodesic.mathdoc.fr/item/DMGT_2001_21_1_a6/

[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.