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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 their conjecture states that the maximum is attained on the clique of order t. We prove the latter 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 conjecture holds whenever t-1r≤...

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

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Publisher copy:
10.1112/jlms.12082

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Institution:
University of Oxford
Division:
MPLS Division
Department:
Mathematical Institute
Role:
Author
Publisher:
Wiley Publisher's website
Journal:
Journal of the London Mathematical Society Journal website
Volume:
96
Issue:
3
Pages:
584-600
Publication date:
2017-10-04
DOI:
EISSN:
1469-7750
ISSN:
0024-6107
Pubs id:
pubs:938249
URN:
uri:907d00e1-0c1b-4e27-b516-d742ab4e695f
UUID:
uuid:907d00e1-0c1b-4e27-b516-d742ab4e695f
Local pid:
pubs:938249

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