The 3/2 conjecture for triangle covering and packing in random graphs

Let $G=G(n,m)$ be a random graph with $n$ vertices and $m$ edges, and let $\tau(G)$ and $\nu(G)$ denote its triangle covering and triangle packing numbers, respectively. For a fixed constant $C>3/2$, consider all values of $m$.

The 3/2 random-graph conjecture. For all $C>3/2$ and $G=G(n,m)$, with high probability,

$$\tau(G)\leq C\cdot\nu(G)$$

for the full range of $m$.

The conjecture is motivated by estimates suggesting that the ratio $\tau(G)/\nu(G)$ grows from about $1$ when triangles first emerge to about $3/2$ in denser random graphs. The source gives this as a possible direction for future study and provides no resolution.