This material has been published in the Journal of Combinatorial Theory, Series A, 93, No. 2, February 2001, 281-291 (doi:10.1006/jcta.2000.3078), the only definitive repository of the content that has been certified and accepted after peer review. Copyright and all rights therein are retained by Academic Press. This material may not be copied or reposted without explicit permission. (Copyright (C) 2001 by Academic Press, Inc.). For Academic Press online journals, see IDEAL (International Digital Electronic Access Library) at http://www.idealibrary.com.

Intersecting Balanced Families of Sets

Adam Idzik,  Gyula O. H. Katona, Rajiv Vohra

Journal of Combinatorial Theory, Series A, 93, 2 (2001), 281-291

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Abstract

Suppose that any t members (t>=2) of a regular family on an n element set have at least k common elements. It is proved that the largest member of the family has at least k1/tn1-1/t. The same holds for balanced families, which is a generalization of the regularity. The estimate is asymptotically sharp.
Copyright 2001 Academic Press.

Key Words:  extremal problems; regular family; balanced family
 

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