How can you find an articulation vertex? — DFS multiple times. Remove each edge one at a time, doing a DFS after each, so see if you end up with > 1 connected components. If you remove a node and then DFS and find you have fewer than m - 1 edges, you've deleted an articulation vertex. O(n(n+m)) A faster way, with a little more bookkeeping, can be done in O(n+m) time, if you do DFS and keep track of parents and make a note when you reach a back edge, which connects to an ancestor.