Hostname: page-component-74656f9884-2dmjx Total loading time: 0 Render date: 2026-11-10T06:04:27.574Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the 'Save PDF' action button.

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 nelements 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.

Information

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