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

Question

Quizplus · Accepted Answer

Both DHAM3 and SHAM3 are NP-hard because determining if a Hamiltonian cycle exists (DHAM3) is a well-known NP-hard problem, and finding such a cycle (SHAM3) is at least as hard, if not harder, than merely determining its existence.

Let SHAM3 Be the Problem of Finding a Hamiltonian Cycle