I know that the following problems related to Hamiltonian paths in graph are NP-complete:Undirected Hamiltonian circuit:Given an undirected graph, does it has a cycle that passes througheach node exactly once?Undirected Hamiltonian path:Given an undirected graph, does it has a path that passes through each node exactly once?Directed Hamiltonian circuit:Given a directed graph, does it has a directed cycle that passes through each node exactly once?But then my textbook says following problems are NP-Hard but not NP-complete:Problem A: Finding a Hamiltonian circuit in a graph with number of vertices $|V|$ divisible by 3Problem B: Determining if Hamiltonian circuit exists in the graphs as given problem A.Why is this so?
Complexity class (P/NP) variants of Hamiltonian paths problems
np complete;np hard;decision problem;complexity classes