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Triple Systems Not Containing a Fano Configuration

Published online by Cambridge University Press:  21 July 2005

ZOLTÁN FÜREDI  and
MIKLÓS SIMONOVITS
ZOLTÁN FÜREDI
Affiliation:
Rényi Institute of Mathematics of the Hungarian Academy of Sciences Budapest, PO Box 127, Hungary-1364 and Department of Mathematics, University of Illinois at Urbana-Champaign Urbana, IL61801, USA (e-mail: [email protected], [email protected])
MIKLÓS SIMONOVITS
Affiliation:
Rényi Institute of Mathematics of the Hungarian Academy of Sciences Budapest, PO Box 127, Hungary-1364 (e-mail: [email protected])
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Abstract

A Fano configuration is the hypergraph of 7 vertices and 7 triplets defined by the points and lines of the finite projective plane of order 2. Proving a conjecture of T. Sós, the largest triple system on $n$ vertices containing no Fano configuration is determined (for $n> n_1$). It is 2-chromatic with $\binom{n}{3}-\binom{\lfloor n/2 \rfloor}{3} -\binom{\lceil n/2 \rceil}{3}$ triples. This is one of the very few nontrivial exact results for hypergraph extremal problems.

Type
Paper
Information
Combinatorics, Probability and Computing , Volume 14 , Issue 4 , July 2005 , pp. 467 - 484
Copyright
© 2005 Cambridge University Press

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