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On Property of Families of Sets

Published online by Cambridge University Press:  20 November 2018

H. L. Abbott
H. L. Abbott*
Affiliation:
University of Alberta Edmonton, Canada and, Massachusetts Institute of Technology Cambridge, Mass. 02139, U.S.A.
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A family of sets is said to have property if there exists a set B such that B ∩ F ≠ Ø and B ⊅ F for every F ∊ . Such a B will be called suitable with respect to F. It is known (see [3]) that for each positive integer n there exists a family of sets satisfying the following conditions:

  1. (a) |F| = n for each F ∊

  2. (b) |F ∩ G| ≤ for F, G ∊ F ≠ G

  3. (c) does not have property

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 18 , Issue 1 , April 1975 , pp. 133 - 135
Copyright
Copyright © Canadian Mathematical Society 1975

References

1. Abbott, H. L. and Hanson, D., On a combinatorial problem of Erdös, Can. Math. Bull. 12 (1969), 823-830.Google Scholar
2. Abbott, H. L., An application of Ramsey's theorem to a problem of Erdös and Hajnal, Can. Math. Bull. 8 (1965), 515-518.Google Scholar
3. Erdös, P. and Hajnal, A., On chromatic numbers of graphs and set systems, Acta Math. Acad. Sci. Hung. 17 (1966), 61-99.Google Scholar
4. Lovász, L., On the chromatic number of finite set systems. Acta Math. Acad. Sci. Hung. 19 (1968), 59-67.Google Scholar
5. Fekete, M., Über die Verteilung der Wurzeln bei gewissen algebraischen Gleichungen mit ganzgahligen Koeffizienten, Math. Zeit. 17 (1923) 228-249.Google Scholar