Which of the following is/are True? I) If P + NP, 3-CLIQUE will be in NP-Complete, but not in NP. II) Hamiltonian path problem is in NP-Complete, as it is in NP and a NP problem can be reduced to Hamiltonian path problem. II) Halting problem is NP-Complete as well as NP-Hard. IV) Euler's circuit problem is in NP, as it can't be solved in polynomial time. A) III and IV B) only II C) only IV D) I and II

Operations Research : Applications and Algorithms
4th Edition
ISBN:9780534380588
Author:Wayne L. Winston
Publisher:Wayne L. Winston
Chapter11: Nonlinear Programming
Section11.11: Separable Programming
Problem 3P
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Which of the following is/are True?
I) If P + NP, 3-CLIQUE will be in NP-Complete, but not in NP.
II) Hamiltonian path problem is in NP-Complete, as it is in NP and a NP problem can be reduced
to Hamiltonian path problem.
II) Halting problem is NP-Complete as well as NP-Hard.
IV) Euler's circuit problem is in NP, as it can't be solved in polynomial time.
A) III and IV
B) only II
C) only IV
D) I and II
Transcribed Image Text:Which of the following is/are True? I) If P + NP, 3-CLIQUE will be in NP-Complete, but not in NP. II) Hamiltonian path problem is in NP-Complete, as it is in NP and a NP problem can be reduced to Hamiltonian path problem. II) Halting problem is NP-Complete as well as NP-Hard. IV) Euler's circuit problem is in NP, as it can't be solved in polynomial time. A) III and IV B) only II C) only IV D) I and II
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