Packing nearly-disjoint sets |
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Authors: | P D Seymour |
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Institution: | (1) Department of Mathematics, The Ohio State University, 43210 Columbus, Ohio, USA |
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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.
Partially supported by N. S. F. grant No. MCS—8103440 |
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Keywords: | 05 C 65 05 C 15 |
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