Geodesic
An Application of Ramsay's Theorem to a Problem of Erdos and Hajnal
Canadian mathematical bulletin, Tome 8 (1965) no. 4, pp. 515-517

Voir la notice de l'article provenant de la source Cambridge University Press

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 (i) |F|=k for each (ii) | F∩ G| ≤ 1 for each F, , F ≠ G (iii) does not possess property ? 
Abbott, H. L. An Application of Ramsay's Theorem to a Problem of Erdos and Hajnal. Canadian mathematical bulletin, Tome 8 (1965) no. 4, pp. 515-517. doi: 10.4153/CMB-1965-038-1
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[1] 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] 2. Erdos, P., On a combinatorial problem. Nordisk. Mat. Tidski, 2 (1963), 5-10. Google Scholar

[3] 3. Erdos, P., Some remarks on the theory of graphs. Bull. Amer. Math. Soc., 53 (1947), 292-294. Google Scholar

[4] 4. Ramsay, F. P., On a problem in formal logic. Proc. London Math. Soc., 30(1930), 264-286. Google Scholar

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