GATE | GATE-CS-2006 | Question 31



Let SHAM3 be the problem of finding a Hamiltonian cycle in a graph G = (V,E) with V divisible by 3 and DHAM3 be the problem of determining if a Hamiltonian cycle exists in such graphs. Which one of the following is true?
(A) Both DHAM3 and SHAM3 are NP-hard
(B) SHAM3 is NP-hard, but DHAM3 is not
(C) DHAM3 is NP-hard, but SHAM3 is not
(D) Neither DHAM3 nor SHAM3 is NP-hard


Answer: (A)

Explanation: The problem of finding whether there exist a Hamiltonian Cycle or not is NP Hard and NP Complete Both.

Finding a Hamiltonian cycle in a graph G = (V,E) with V divisible by 3 is also NP Hard.

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