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Hypergraph Lagrangians I: The Frankl-Füredi conjecture is false

Gruslys, V; Letzter, S; Morrison, N; (2020) Hypergraph Lagrangians I: The Frankl-Füredi conjecture is false. Advances in Mathematics , 365 , Article 107063. 10.1016/j.aim.2020.107063. Green open access

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Abstract

An old and well-known conjecture of Frankl and F¨uredi states that the Lagrangian of an r-uniform hypergraph with m edges is maximised by an initial segment of colex. In this paper we disprove this conjecture by finding an infinite family of counterexamples for all r ≥ 4. We also show that, for sufficiently large t ∈ N, the conjecture is true in the range e (t r) ≤ m ≤ ( t+1 r ) − ( t−1 r−2 )

Type: Article
Title: Hypergraph Lagrangians I: The Frankl-Füredi conjecture is false
Open access status: An open access version is available from UCL Discovery
DOI: 10.1016/j.aim.2020.107063
Publisher version: http://dx.doi.org/10.1016/j.aim.2020.107063
Language: English
Additional information: This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions.
Keywords: Lagrangians, Hypergraphs, Extremal combinatorics
UCL classification: UCL
UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics
URI: https://discovery.ucl.ac.uk/id/eprint/10107222
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