A note on kernels and solutions in digraphs

• Autorzy: Matúš Harminc , Roman Soták
• Języki publikacji: EN

Abstrakty

EN

For given nonnegative integers k,s an upper bound on the minimum number of vertices of a strongly connected digraph with exactly k kernels and s solutions is presented.

Słowa kluczowe

EN

kernel of digraph; solution of digraph

Kategorie tematyczne

• 05C20: Directed graphs (digraphs), tournaments

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 1999
• Tom: 19
• Numer: 2
• Strony: 237-240

Daty

wydano

1999

otrzymano

1999-02-02

poprawiono

1999-10-29

Twórcy

autor

Matúš Harminc

• Department of Geometry and Algebra, Faculty of Science, P.J. Šafárik University, Jesenná 5, 041 54 Košice, Slovakia

autor

Roman Soták

• Center of applied informatics, Faculty of Science, P.J. Šafárik University, Park Angelinum 9, 041 54 Košice, Slovakia

Bibliografia

• [1] M. Behzad and F. Harary, Which directed graphs have a solution?, Math. Slovaca 27 (1977) 37-42.
• [2] V.V. Belov, E.M. Vorobjov and V.E. Shatalov, Graph Theory (Vyshshaja Shkola, Moskva, 1976). (Russian)
• [3] C. Berge, Graphs and Hypergraphs (Dunod, Paris, 1970). (French)
• [4] M.R. Garey and D.S. Johnson, Computers and Intractability, A Guide to the Theory of NP-Completeness (Freeman, San Francisco, 1979).
• [5] F. Harary, R.Z. Norman and D. Cartwright, Structural Models (John Wiley & Sons, Inc., New York - London - Sydney, 1965).
• [6] M. Harminc, Kernel and solution numbers of digraphs, Acta Univ. M. Belii 6 (1998) 15-20.
• [7] M. Harminc and T. Olejnikova, Binary operations on digraphs and solutions, Zb. ved. prac, VST, Košice (1984) 29-42. (Slovak)
• [8] L. Lovasz, Combinatorial Problems and Exercises (Akademiai Kiado, Budapest, 1979).
• [9] R.G. Nigmatullin, The largest number of kernels in graphs with n vertices, Kazan. Gos. Univ. Ucen. Zap. 130 (1970) kn.3, 75-82. (Russian)

Identyfikatory

DOI

10.7151/dmgt.1098