For an arbitrary simple finite graph $G$, without multiple edges between any two nodes and without any loop, the minimum induced subtree cover number, which is denoted by $stc(G)$, is defined to be the minimum number of induced sub-trees of $G$ without any edge intersection that cover the whole graph $G$;e.g, contains all edges of $G$. Let $E(G)$ denotes the number of edges of the graph $G$. It is easy to see that $$1\leq stc(G)\leq |E(G)|.$$
My question is: For a random graph $G(p)$ with $n$ vertices and the probability of $p$ for existence an edge between two arbitrary nodes, what is the $stc(G(p))$ approximately?
