Erdős Problem #1158

Let $K_{t}(r)$ be the complete $t$-partite $t$-uniform hypergraph with $r$ vertices in each class.

Is it true that\[\mathrm{ex}_t(n,K_t(r)) \geq n^{t-r^{1-t}-o(1)}\]for all $t,r$?

#1158: [Va99,3.65]

hypergraphs | turan number

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Erdős [Er64f] proved that\[n^{t-O(r^{1-t})}\leq \mathrm{ex}_t(n,K_t(r)) \ll n^{t-r^{1-t}}.\]This is only known when $t=2$ and $2\leq r\leq 3$. The case $t=2$ is [714].

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This page was last edited 23 January 2026.

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