Tarjan's Algorithm for Articulation Points

Tarjan's algorithm finds all articulation points in $O(V+E)$ time using the same DFS approach. A vertex $u$ is an articulation point if:

$1.$ $u$ is the root of the DFS tree and has $\geq 2$ children (root case), OR

$2.$ $u$ is not the root and has a child $v$ where low[v] >= disc[u] (non-root case).

Note: $\geq$ not $>$ like bridges. Equality means the subtree can reach $u$ but not beyond, so $u$ is still critical.

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