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<j ≦k, 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.
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References
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Partially supported by N. S. F. grant No. MCS—8103440