An assignment question asks,
Given a connected, undirected graph $G$, describe an algorithm which can determine if the removal of any pair of vertices would cause $G$ to become disconnected.
There is an obvious brute force solution, which is to just generate all pairs of vertices, produce new graphs with those vertices removed, and then test if that graph is connected using something like a BFS, running in $O(|V|^3)$ time.
However, I feel like this is not the intent of the question. We learned about an algorithm to find the articulation points of a graph, and it seems like something like this should be possible to determine if the removal of any pair of vertices would disconnect the graph, but I am not sure how it would be applicable.