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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

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✦ 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.


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