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Degrees giving independent edges in a hypergraph

Published online by Cambridge University Press:  17 April 2009

David E. Daykin
Affiliation:
Department of Mathematics, University of Reading, Whiteknights, Reading, Berkshire RG6 2AX, England
Roland Häggkvist
Affiliation:
Institut Mittag-Leffler, Auravägen 17, S-182 62 Djursholm, Sweden.
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Abstract

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For r-partite and for r-uniform hypergraphs bounds are given for the minimum degree which ensures d independent edges.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1981

References

[1]Bollobás, B., Daykin, D.E. and Erdös, P., “Sets of independent edges in a hypergraph”, Quart. J. Math. Oxford Ser. (2) 27 (1976), 2532.CrossRefGoogle Scholar
[2]Brace, Alan, “Some combinatorial cover theorems” (PhD thesis, University of Western Australia, Nedlands, 1971).Google Scholar
[3]Brace, Alan and Daykin, D.E., “A finite set covering theorem”, Bull. Austral. Math. Soc. 5 (1971), 197202.CrossRefGoogle Scholar
[4]Brace, Alan and Daykin, D.E., “A finite set covering theorem II”, Bull. Austral. Math. Soc. 6 (1972), 1924.CrossRefGoogle Scholar
[5]Brace, Alan and Daykin, D.E., “A finite set covering theorem III”, Bull. Austral. Math. Soc. 6 (1972), 417433.CrossRefGoogle Scholar
[6]Brace, A., Daykin, D.E., “A finite set covering theorem. IV”, Infinite and finite sets, Vol. I, 199203 (Colloq., Keszthely, 1973. Colloq. Math. Soc. J´anos Bolyai. 10. North-Holland, Amsterdam, 1975).Google Scholar
[7]Brace, Alan, Daykin, D.E., “Sperner type theorems for finite sets”, Combinatorics, 1837 (Proc. Conf. Combinatorial Math., Math. Inst., Oxford, 1972. Inst. Math. Appl., Southend-on-Sea, 1972).Google Scholar
[8]Daykin, D.E., “Minimum subcover of a cover of a finite set”, Problem, Amer. Math. Monthly 85 (1978), 766.CrossRefGoogle Scholar