Jie Ma of Tsinghua University : Extremal hypergraphs without generalized $4$-cycles

Posted by Dhruv Mubayi , part of the Mathematical Computer Science Seminar.

At

Oct. 5, 2026, 3 p.m.

In

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Abstract

In 1977, Erd\H{o}s posed the problem of determining the maximum number $f_r(n)$ of edges in an $n$-vertex $r$-uniform hypergraph in which all disjoint pairs of edges have distinct unions. F\"uredi later conjectured that, for every fixed $r\ge 4$ and all sufficiently large $n$, $f_r(n)=\binom{n-1}{r-1}+\lfloor \frac{n-1}{r}\rfloor$. In this paper, we prove this conjecture and determine all extremal configurations. Our proof combines a stability theorem for such dense hypergraphs with a delicate deletion argument applied to an associated bipartite $3$-graph. The stability theorem also resolves a conjecture of Mubayi.