Articulation Point: Non-Root Case

For a non-root vertex $u$ with child $v$ in the DFS tree: If low[v] >= disc[u], then $u$ is an articulation point. Why? low[v] >= disc[u] means the subtree rooted at $v$ cannot reach any vertex discovered before $u$.

The subtree can reach $u$ (when low[v] = disc[u]) or only later vertices (when low[v] > disc[u]). Either way, $u$ is the gateway. Remove $u$, and the subtree disconnects.