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Lagrangians of hypergraphs: The Frankl-Füredi conjecture holds almost everywhere

Abstract:

Frankl and Füredi conjectured in 1989 that the maximum Lagrangian of all r-uniform hypergraphs of fixed size m is realised by the initial segment of the colexicographic order. In particular, in the principal case m=(tr) that every H⊆N(r)of size (tr) satisfies max⁡{∑A∈H∏i∈Ayi:y1,y2,…≥0;∑i∈Nyi=1}≤[Formula presented](tr). We prove the above statement for all r≥4 and large values of t (the case r = 3 was settled by Talbot in 2002). More generally, we show for any r≥4 that the Frankl-Füredi conjec...

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Publication status:
Published
Peer review status:
Peer reviewed
Version:
Accepted Manuscript

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Publisher copy:
10.1016/j.endm.2017.07.072

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Institution:
University of Oxford
Division:
MPLS Division
Department:
Mathematical Institute
Publisher:
Elsevier Publisher's website
Journal:
Electronic Notes in Discrete Mathematics Journal website
Volume:
61
Pages:
1055-1059
Publication date:
2017-08-03
DOI:
ISSN:
1571-0653
Pubs id:
pubs:938279
URN:
uri:3e8094d6-8624-4e38-8bfa-4e0f1db5c18a
UUID:
uuid:3e8094d6-8624-4e38-8bfa-4e0f1db5c18a
Local pid:
pubs:938279

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