Lagrangians of Hypergraphs II: When colex is best

2019/07/23 by Gruslys, Vytautas, Letzter, Shoham, Morrison, Natasha · 1 citation
#05C35 #05C65 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.1907.09797

Abstract

A well-known conjecture of Frankl and Füredi from 1989 states that an initial segment of colex of 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 and a counterexample to an old conjecture of Ahlswede and Katona.

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• The Erdős--Ko--Rado Theorem in ℓ₂-Norm

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