# undirected graph without weights and DFS [closed]

following question on undirected graph without weights can be solved by using DFS and in O(|V|+|E|) times.

1. check that G is bipartite.

2. check G has one simple cycle.

3. find number of connected component G

4. with given two vertex u, v, find a path between u and v with minimum edges

anyone can describe, how the authors of this note claim that all of them can be checked with DFS and in O(|V|+|E|) times?

## closed as too broad by Juho, David Richerby, Luke Mathieson, D.W.♦, Carlos Linares LópezFeb 28 '15 at 23:20

Please edit the question to limit it to a specific problem with enough detail to identify an adequate answer. Avoid asking multiple distinct questions at once. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.

• Whom are the authors? I think that you can split you're question in a least four. – jonaprieto Feb 28 '15 at 8:08