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Packing nearly-disjoint sets
Authors:P D Seymour
Institution:(1) Department of Mathematics, The Ohio State University, 43210 Columbus, Ohio, USA
Abstract:De Bruijn and Erdős proved that ifA 1, ...,A k are distinct subsets of a set of cardinalityn, and |A i A j |≦1 for 1≦i<jk, andk>n, then some two ofA 1, ...,A k have empty intersection. We prove a strengthening, that at leastk /n ofA 1, ...,A k are pairwise disjoint. This is motivated by a well-known conjecture of Erdőds, Faber and Lovász of which it is a corollary. Partially supported by N. S. F. grant No. MCS—8103440
Keywords:05 C 65  05 C 15
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