I am trying to find how close $tw(G)$ and $E[tw(G)]$ really are, when $G \in G(n,p=c/n)$and $c>1$ is a constant not depending on n (so $E[tw(G)] = \Theta(n)$). My estimate is that $tw(G) \leq E[tw(G)] + o(n)$ w.h.p, but i haven't been able to prove it.
How big is the variance of the treewidth of a random graph in G(n,p)?
graph theory;co.combinatorics;treewidth;random graphs