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An Application of Ramsay's Theorem to a Problem of Erdos and Hajnal

Published online by Cambridge University Press:  20 November 2018

H. L. Abbott
H. L. Abbott*
Affiliation:
University of Alberta, Edmonton
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A family of sets is said to possess property if there exists a set such that and F ⊄ B for each In [1], P. Erdos and A. Hajnal ask the following question: Does there exist for every positive integer k a finite family of finite sets satisfying

  1. (i) |F|=k for each

  1. (ii) | F∩ G| ≤ 1 for each F, , F ≠ G

  1. (iii) does not possess property ?

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 8 , Issue 4 , June 1965 , pp. 515 - 517
Copyright
Copyright © Canadian Mathematical Society 1965

References

1. Erdos, P. and Hajnal, A. On a property of families of sets. Acta, Math. Acad., Hung. Sci. 12(1961), 87-123.Google Scholar
2. Erdos, P., On a combinatorial problem. Nordisk. Mat. Tidski, 2 (1963), 5-10.Google Scholar
3. Erdos, P., Some remarks on the theory of graphs. Bull. Amer. Math. Soc., 53 (1947), 292-294.Google Scholar
4. Ramsay, F. P., On a problem in formal logic. Proc. London Math. Soc., 30(1930), 264-286.Google Scholar