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An extremal problem in graph theory II

Part of: Graph theory

Published online by Cambridge University Press:  09 April 2009

H. L. Abbott ,
M. Katchalski  and
A. C. Liu
H. L. Abbott
Affiliation:
Mathematics Department University of AlbertaEdmonton, CanadaT6G 2G1
M. Katchalski
Affiliation:
Mathematics Department Technion Haifa, Israel
A. C. Liu
Affiliation:
Mathematics Department University of ReginaRegina, CanadaS4S 0A2
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Abstract

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We contine our study of the following combinatorial problem: What is the largest integer N = N (t, m, p) for which there exists a set of N people satisfying the following conditions: (a) each person speaks t languages, (b) among any m people there are two who speak a common language and (c) at most p speak a common language. We obtain bounds for N(t, m, p) and evaluate N(3, m, p) for all m and infintely many values of p.

MSC classification

Secondary: 05C35: Extremal problems
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 29 , Issue 4 , June 1980 , pp. 417 - 424
Copyright
Copyright © Australian Mathematical Society 1980

References

Abbott, H. L., Hanson, D. and Liu, A. C., ‘An extremal problem in graph theory’, Quart. J. Math. Oxford Ser. (to appear).Google Scholar
Béla, Bollobás (1977), ‘Disjoint triples in a 3-graph with given maximal degree’, Quart. J. Math. Oxford Ser. 28, 81–85.Google Scholar