2025/03/26 by Gishboliner, Lior, Honest, Ethan
#Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.2503.21052
For ℓ ≥ 3, an ℓ-uniform hypergraph is disperse if the number of edges induced by any set of ℓ+1 vertices is 0, 1, ℓ or ℓ+1. We show that every disperse ℓ-uniform hypergraph on n vertices contains a clique or independent set of size n^Ωℓ(1), answering a question of the first author and Tomon. To this end, we prove several structural properties of disperse hypergraphs.