# 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?

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