Hi i have these two problems that are part of a practice set i am doing for exams, i can't seem to get around them. If you can answer any of them thanks in advance.
- For a given graph $G=(V,E)$ and an edge $e\in E$, design an $O(n+m)$-time algorithm to find, if it exists, the shortest cycle that contains $e$.
2. (a) Prove that every connected graph $G=(V,E)$ has a node $v\in V$ such that removing $v$ and all its adjacent edges will not disconnect $G$.
(b) For a given connected graph $G=(V,E)$, design an $O(n+m)$-time algorithm to find such a node.