Data Structures and Algorithms #3
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.
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1 solution
1 is true because cycle detection can be done in polynomial time using DFS (See this).
2 is true because P is a subset of NP.
3 is true because NP complete is also a subset of NP and NP means Non-deterministic Polynomial time solution exists.
(SOURCE: http://en.wikipedia.org/wiki/NP_(complexity) )