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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.

1. 1, 2 and 3
2. 1 and 2 only
3. 2 and 3 only
4. 1 and 3 only

Correct answer: 1, 2 and 3

Solution

All three statements are true: determining the existence of a cycle in an undirected graph can be solved in polynomial time (making it in P), it is also verifiable in polynomial time (placing it in NP), and NP-Complete problems have non-deterministic polynomial time algorithms, which is a defining characteristic.

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