The Maximum Size of 3-Uniform Hypergraphs Not Containing a Fano Plane

The Maximum Size of 3-Uniform Hypergraphs Not Containing a Fano Plane

A conjecture of V. Sós [3] is proved that any set of 34 (n3)+cn2 triples from an n-set, where c is a suitable absolute constant, must contain a copy of the Fano configuration (the projective plane of order two). This is an asymptotically sharp estimate.

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Veröffentlicht in:Journal of combinatorial theory. Series B 2000-03, Vol.78 (2), p.274-276
Hauptverfasser: De Caen, Dominique, Füredi, Zoltán
Format: Artikel
Sprache:eng
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Zusammenfassung:A conjecture of V. Sós [3] is proved that any set of 34 (n3)+cn2 triples from an n-set, where c is a suitable absolute constant, must contain a copy of the Fano configuration (the projective plane of order two). This is an asymptotically sharp estimate.
ISSN:0095-8956
1096-0902
DOI:10.1006/jctb.1999.1938