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Lagrangians of Hypergraphs II: When colex is best

Gruslys, V; Letzter, S; Morrison, N; (2021) Lagrangians of Hypergraphs II: When colex is best. (In press).

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Abstract

A well-known conjecture of Frankl and F¨uredi from 1989 states that an initial segment of the colexicographic order has the largest Lagrangian of any r-uniform hypergraph with m hyperedges. We show that this is true when r = 3. We also give a new proof of a related conjecture of Nikiforov for large t and a counterexample to an old conjecture of Ahlswede and Katona.

Type: Article
Title: Lagrangians of Hypergraphs II: When colex is best
Publisher version: https://arxiv.org/abs/1907.09797
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.
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/10107290
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