Geodesic
On Property B of Families of Sets
Canadian mathematical bulletin, Tome 23 (1980) no. 4, pp. 429-435

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

A family of sets is said to have property B if there exists a set S such that S∩F≠ φ and SF for all F . S is called a B-set for . Let n≥2 and N≥2n-1. Let V = { 1, 2,≠, N} and let = {G:G⊂ V, |G| = rc}. Erdös [3] defined mN(n) to be the size of a smallest subfamily of which does not have property B and proved the following results: 
Abbott, H. L.; Liu, A. C. On Property B of Families of Sets. Canadian mathematical bulletin, Tome 23 (1980) no. 4, pp. 429-435. doi: 10.4153/CMB-1980-063-6
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[1] 1. Abbott, H. L. and Moser, L.. On a combinatorial problem of Erdôs and Hajnal, Can. Math. Bull., 7 (1964), 177-181. Google Scholar

[2] 2. De Vries, H. L.. On property B and on Steiner systems, Math. Zeit., 53 (1977), 155-159. Google Scholar

[3] 3. Erdôs, P.. On a combinatorial problem III, Can. Math. Bull. 12 (1969), 413-416. Google Scholar

[4] 4. Spencer, J.. Puncture sets, J. Comb. Theory, A17 (1974), 329-336. Google Scholar

[5] 5. Stein, S. K.. Two combinatorial covering theorems, J. Comb. Theory, A16 (1974), 391-397. Google Scholar

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