Geodesic
On a Combinatorial Problem of Erdös and Hajnal
Canadian mathematical bulletin, Tome 7 (1964) no. 2, pp. 177-181

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

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. 
Abbott, H. L.; Moser, L. On a Combinatorial Problem of Erdös and Hajnal. Canadian mathematical bulletin, Tome 7 (1964) no. 2, pp. 177-181. doi: 10.4153/CMB-1964-016-9
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[1] 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] 2. Erdös, P., On a combinatorial problem, Nordisk Mat. Tidski. 2 (1963) pp.5–10. Google Scholar

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