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Claim. For $r=2$ the question of Problem 719 asks whether every graph on $n$ vertices is the union of at most $\mathrm{ex}_2(n;K_3)=\lfloor n^2/4\rfloor$ edges and triangles, no two sharing an edge. Theorem 4 of Erdős, Goodman and Pósa's paper (p. 108) states that every graph of order $n\ge2$ with no isolated point is covered by at most $\lfloor n^2/4\rfloor$ complete subgraphs, no two with an edge in common, all of them edges or triangles; the proof is an induction on $n$ that removes a vertex of smallest degree, returning its edges as single edges or, when the degree exceeds $\lfloor n/2\rfloor$, as triangles through independent edges among its neighbors. Isolated vertices change nothing: the graph induced on the $n'\le n$ non-isolated vertices has at most $\lfloor n'^2/4\rfloor\le\lfloor n^2/4\rfloor$ pieces, and a graph with no edge is the empty union. The bound is sharp for the complete bipartite graph with parts as equal as possible, which has $\lfloor n^2/4\rfloor$ edges and no triangle, so the question's bound cannot be lowered at $r=2$. Erdős restates the theorem in [Er81], Part IV, item 3, as the model for the conjecture with Sauer for general $r$, which is the problem's statement.

Covers. The case $r=2$ for every $n$. It says nothing about any $r\ge3$, where the hypergraph Turán numbers $\mathrm{ex}_r(n;K_{r+1}^r)$ are themselves unknown.

Acceptance. Refereed: Canad. J. Math. 18 (1966), 106–112, Theorem 4 on p. 108, as the library result page records. The publication record gives only the year, so the page is dated to the first day of it. The site's commentary credits no result on the problem and labels it OPEN, so the page lists no reviewed; the standing of the problem is unchanged by this partial claim.