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GATE | GATE CS 2013 | Question 18

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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

Answer: (A)

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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Last Updated : 28 Jun, 2021
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