Erdős Problem #719 — Let ex_r(n;K_r+1^r) be the maximum number of r-edges that can be placed on n vertices without forming a K_r+1^r (the r-uniform complete graph on r+1 vertices).

Question

Let ex_r(n;K_r+1^r) be the maximum number of r-edges that can be placed on n vertices without forming a K_r+1^r (the r-uniform complete graph on r+1 vertices). Is every r-hypergraph G on n vertices the union of at most ex_r(n;K_r+1^r) many copies of K_r^r and K_r+1^r, no two of which share a K_r^r?

Erdős Problem #719 — Let $\mathrm{ex}_r(n;K_{r+1}^r)$ be the maximum number of $r$ -edges that can be placed on $n$ vertices without forming a $K_{r+1}^r$ (the $r$ -uniform complete graph on $r+1$ vertices).

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