# GATE | GATE CS 2013 | Question 18

Which of the following statements are TRUE?

```1. The problem of determining whether there exists
a cycle in an undirected graph is in P.
2. The problem of determining whether there exists
a cycle in an undirected graph is in NP.
3. If a problem A is NP-Complete, there exists a
non-deterministic polynomial time algorithm to solve A. ```

(A) 1, 2 and 3
(B) 1 and 2 only
(C) 2 and 3 only
(D) 1 and 3 only

Explanation: 1. We can either use BFS or DFS to find whether there is a cycle in an undirected graph. For example, see DFS based implementation to detect cycle in an undirected graph. The time complexity is O(V+E) which is polynomial.

2. If a problem is in P, then it is definitely in NP (can be verified in polynomial time). See NP-Completeness

3. True. See See NP-Completeness

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