Let SHAM3 Be the Problem of Finding a Hamiltonian Cycle

question 1

Multiple Choice

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