The Brown-Erdős-Sós conjecture in dense triple systems

2025/08/13 by Santos, Giovanne, Tyomkyn, Mykhaylo
#Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2508.09841

Abstract

The famous Brown-Erdős-Sós conjecture from 1973 states, in an equivalent form, that for any fixed δ>0 and integer k≥ 3 every sufficiently large linear 3-uniform hypergraph of size δn² contains some k edges spanning at most k+3 vertices. We prove it to hold for δ>4/5, establishing the first bound of this kind.

Citations

• The (7,4)-conjecture in finite groups

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