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On a Combinatorial Problem of Erdös and Hajnal

Published online by Cambridge University Press:  20 November 2018

H. L. Abbott  and
L. Moser
H. L. Abbott
Affiliation:
University of Alberta, Edmonton
L. Moser
Affiliation:
University of Alberta, Edmonton
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In this note we consider some problems related to the following question: What is the smallest integer m(n) for which there exists a family Fn of sets A1, A2,…, Am(n) with the following properties, (i) each member of Fn has n elements and (ii) if S is a set which meets each member of Fn, then S contains at least one member of Fn?

Erdős and Hajnal [1] observed that

and that m(l) = 1, m(2) = 3, m(3) = 7.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 7 , Issue 2 , June 1964 , pp. 177 - 181
Copyright
Copyright © Canadian Mathematical Society 1964

References

1. Erdös, P. and Hajnai, A., On a property of families of sets, Acta. Math. Acad. Hung. Sci. 12(1961) pp.87–123.Google Scholar
2. Erdös, P., On a combinatorial problem, Nordisk Mat. Tidski. 2 (1963) pp.5–10.Google Scholar