Tarjan's Algorithm for Bridges

Tarjan's algorithm finds all bridges in $O(V+E)$ time using a single DFS traversal. The idea: run DFS, compute disc[v] and low[v] for each vertex. An edge $(u, v)$ is a bridge if low[v] > disc[u]. Why?

If low[v] > disc[u], then the subtree rooted at $v$ cannot reach any vertex discovered before $u$ or even $u$ itself. The edge $(u, v)$ is the only connection. Remove it, and the subtree becomes isolated.

Space complexity is $O(V)$ for the data structures used.