Author

Oleg Pikhurko

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Preprint Oct 2026

The quadratic Brown--Erd\H{o}s--S\'os problem for 3-uniform hypergraphs with 8 and 9 edges

The famous and actively studied problem of Brown--Erd\H{o}s--S\'os from 1973 asks for $f^{(r)}(n;s,k)$, the maximum number of edges in an $r$-graph with $n$ vertices in which no $s$ vertices span $k$ or more edges. In this paper, we concentrate on the case $r=3$ and $s=k+2$, with $k\ge2$ fixed and $n\to\infty$; then it...

Levente Bodnár, Oleg Pikhurko, Shu-Min Sun et al. · 0 citations

Preprint Aug 2026

An improved bound on the minimum size of Tur\'an $(r+1,r)$-systems

For positive integers $n\ge s>r$, let $T(n,s,r)$ denote the minimum number of edges in an $r$-uniform hypergraph on $n$ vertices such that every $s$-set of vertices contains at least one edge. A simple averaging argument shows that the ratio $T(n,s,r)/\binom nr$ is non-decreasing in $n$ and we denote its limit as $n\to...

Jun Gao, Pei-Ru Kuang, Oleg Pikhurko et al. · 0 citations