Q. 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