Mathematical Computer Science Seminar: Extremal hypergraphs without generalized $4$-cycles, by Jie Ma
Mathematical Computer Science Seminar
October 5, 2026
3:00 PM - 4:00 PM
Location
427 SEO
Calendar
Download iCal FileJie Ma, Tsinghua University: Extremal hypergraphs without generalized $4$-cycles
In 1977, ErdH{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 $rge 4$ 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.
Date posted
Oct 5, 2026
Date updated
Oct 5, 2026