# A note on kernels and solutions in digraphs

Discussiones Mathematicae Graph Theory (1999)

- Volume: 19, Issue: 2, page 237-240
- ISSN: 2083-5892

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topMatúš Harminc, and Roman Soták. "A note on kernels and solutions in digraphs." Discussiones Mathematicae Graph Theory 19.2 (1999): 237-240. <http://eudml.org/doc/270700>.

@article{MatúšHarminc1999,

abstract = {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.},

author = {Matúš Harminc, Roman Soták},

journal = {Discussiones Mathematicae Graph Theory},

keywords = {kernel of digraph; solution of digraph; strongly connected digraph; kernels},

language = {eng},

number = {2},

pages = {237-240},

title = {A note on kernels and solutions in digraphs},

url = {http://eudml.org/doc/270700},

volume = {19},

year = {1999},

}

TY - JOUR

AU - Matúš Harminc

AU - Roman Soták

TI - A note on kernels and solutions in digraphs

JO - Discussiones Mathematicae Graph Theory

PY - 1999

VL - 19

IS - 2

SP - 237

EP - 240

AB - 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.

LA - eng

KW - kernel of digraph; solution of digraph; strongly connected digraph; kernels

UR - http://eudml.org/doc/270700

ER -

## References

top- [1] M. Behzad and F. Harary, Which directed graphs have a solution?, Math. Slovaca 27 (1977) 37-42. Zbl0368.05027
- [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). Zbl0411.68039
- [5] F. Harary, R.Z. Norman and D. Cartwright, Structural Models (John Wiley & Sons, Inc., New York - London - Sydney, 1965). Zbl0139.41503
- [6] M. Harminc, Kernel and solution numbers of digraphs, Acta Univ. M. Belii 6 (1998) 15-20. Zbl0921.05037
- [7] M. Harminc and T. Olejnikova, Binary operations on digraphs and solutions, Zb. ved. prac, VST, Košice (1984) 29-42. (Slovak) Zbl0586.05018
- [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) Zbl0216.02502

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