Open. What is known: the universal bound $f(n,k)\le[n^2/4]$ with edges and triangles only (Theorem 4 (Erdős, Goodman and Pósa 1966) of [EGP66], Canad. J. Math. 1966, refereed); the origin passages of 1966 and 1971 with Lovász's covering bound quoted by Erdős (Lovász's paper [Lo68] is not held); and the $K_4$-free case, in which a partition uses only edges and triangles and minimizing pieces is the same as packing edge-disjoint triangles: Theorem 1 (Győri and Keszegh 2017) of [GyKe17] (Combinatorica 2017, refereed; cited from arXiv v1) gives at least $\lceil k\rceil$ edge-disjoint triangles in every $K_4$-free graph with $n^2/4+k$ edges, sharp for $k$ up to about $n^2/16$ (equality for a Turán graph with a triangle-free graph inside one side), so such a graph is partitioned into at most $n^2/4-k$ pieces (a one-line conversion made below), the exact $K_4$-free minimum in that range; between about $n^2/16$ and the $K_4$-free maximum $n^2/12$ only this upper bound is known, and the authors conjecture a stronger one. The same conversion holds for every graph: $\tau$ edge-disjoint triangles leave a partition into $e-2\tau$ triangles and edges, so packing theorems for general graphs sharpen $[n^2/4]$. Write $[n^2/4]+m$ for the number of edges. Győri's exact result as [BaWi25] restates it on p. 10 ($m$ edge-disjoint triangles when $m\le2n-10$ for odd $n$ or $m\le1.5n-5$ for even $n$; Erdős stated the case $m<cn$ in item 3 of [Er71], naming the method but printing no proof) gives $f=[n^2/4]-m$ in that range. Equality is attained by the Győri--Keszegh equality graphs: a Turán graph with a triangle-free graph of $m$ edges inside one side, in which every triangle uses one of those $m$ edges. Győri's Theorem 1.6 as [BaWi25] restates it gives $f=[n^2/4]-m+O(m^2/n^2)$ for $m=o(n^2)$. Conjecture 1.4, which [BaWi25] proves from its Theorem 1.8, gives $f\le[n^2/4]-(1/3-o(1))m$ for every $m$. These are authored conversions. For $m$ of order $n^2$ no estimate beyond these bounds was found in the search whose scope the Current assessment records; this is a bounded negative finding, not a certificate of openness.