A family F of sets is s-disjointly representable if there is a family 9 of disjoint sets each of size s such that every F is an element of F contains some S is an element of F. Let f (r, s) be the minimum size of a family F of r-sets which is not s-disjointly representable. We give upper and lower bounds on f(r,s) which are within a constant factor when s is fixed. (C) 2003 Elsevier Science (USA). All rights reserved. [References: 10]
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