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An extremal problem in hypergraph theory (II)

Part of: Graph theory

Published online by Cambridge University Press:  09 April 2009

H. L. Abbott ,
D. Hanson  and
A. C. Liu
H. L. Abbott
Affiliation:
Mathematics Department, University of Alberta, Edmonton, Alberta, Canada
D. Hanson
Affiliation:
Department of Mathematics, University of Regina, Regina, Canada S4S 0A2
A. C. Liu
Affiliation:
Mathematics Department, University of Alberta, Edmonton, Alberta, Canada
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Abstract

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Let t, m > 2 and p > 2 be positive integers and denote by N(t, m, p) the largest integer for which there exists a t-uniform hypergraph with N (not necessarily distinct) edges and having no independent set of edges of size m and no vertex of degree exceeding p. In this paper we complete the determination of N(t, m, 3) and obtain some new bounds on N(t, 2, p).

MSC classification

Secondary: 05C65: Hypergraphs
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 31 , Issue 2 , August 1981 , pp. 129 - 135
Copyright
Copyright © Australian Mathematical Society 1982

References

[1]Abbott, H. L., Hanson, D. and Liu, A. C., ‘An extremal problem in graph theory’, Quart. J. Math., Oxford Ser. 131, 121, 1980.Google Scholar
[2]Abbott, H. L., Katchalski, M. and Liu, A. C., ‘An extremal problem in graph theory II’, J. Austral. Math. Soc., (to appear).Google Scholar
[3]Abbott, H. L., Katchalski, M. and Liu, A. C., ‘An extremal problem in hypergraph theory’, Discrete Mathematical Analysis and Combinatorial Computation, Conference proceedings, School of Computer Science, University of New Brunswick, Fredericton, (1980) pp. 74–82.Google Scholar