Articulation Point Walkthrough

Graph: $0-1$, $1-2$, $0-2$, $1-3$. Start DFS at $0$. Visit $0$: disc[0]=0. Visit $1$: disc[1]=1. Visit $2$: disc[2]=2. Back edge $2-0$: low[2]=0. Backtrack: low[1]=0. Visit $3$: disc[3]=3, low[3]=3. Backtrack: check low[3]=3 >= disc[1]=1, so $1$ is an articulation point.

Root $0$ has only $1$ child, so not an articulation point. Final articulation points: $\{1\}$. Removing $1$ splits the graph into $\{0,2\}$ and $\{3\}$.