Bridge Detection Logic

For each tree edge $(u, v)$ where $u$ is the parent of $v$ in the DFS tree: Check if low[v] > disc[u]. If yes, $(u, v)$ is a bridge. Why? low[v] > disc[u] means the subtree of $v$ cannot reach $u$ or any ancestor of $u$.

The edge $(u, v)$ is the only connection between the subtree and the rest of the graph. If low[v] <= disc[u], then there is a back edge providing an alternate path, so $(u, v)$ is not a bridge.