On maximal intersecting families of finite sets |
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Authors: | Zoltán Füredi |
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Affiliation: | Mathematical Institute of the Hungarian Academy of Sciences, V. Realtanoda u. 13-15, Budapest, Hungary |
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Abstract: | Let r be a positive integer. A finite family of pairwise intersecting r-sets is a maximal clique of order r, if for any set A ? , |A| ? r there exists a member E ? such that . For instance, a finite projective plane of order r ? 1 is a maximal clique. Let N(r) denote the minimum number of sets in a maximal clique of order r. We prove whenever a projective plane of order exists. This disproves the known conjecture N(r) ? r2 ? r + 1. |
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