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.
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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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