Given a connected and directed graph $G=(V,E)$ with positive weights on the edges. for every $t>0$ we define $E(t)$ to be the group of edges with weight lower or equal than $t$. I need to find an efficient algorithm which computes the minimal $t$ such that $G(t)=(V,E(t))$ is connected.
I can sort all the edges with $|E|\log|E|$ complexity and try to take edges out of the graph from the heaviest to the easiet one, and to check with DFS if it is still connected, but its not effiecnt enough,
Any suggestions?