On finite set-systems whose every intersection is a Kernel of a star

✍ Scribed by Z. Füredi

• Publisher: Elsevier Science
• Year: 1983
• Tongue: English
• Weight: 344 KB
• Volume: 47
• Category: Article
• ISSN: 0012-365X
• DOI: 10.1016/0012-365x(83)90081-x

✦ Synopsis

Let k, t be positive integers and let 9 be a set-system which consists of k-element sets. In this paper it is proved that one can choose a subsystem 9* c 9F containing a positive proportion of the members of 9, (i.e. 145*1 >c(k, t) IsSj) and having the property that every pairwise intersection is a kernel of a t-star in 9F* (i.e. VF, F'E 9r*, FII F' = A, 3F1, . . . , F, ES* such that F,nF,=A for l<i<j<t). This result is used to obtain some new bounds for the maximum cardinality of a k-graph with prescribed cardinalities for pairwise intersections.