In the context of a Hamiltonian problem, which of the following are correct?

A. Hamiltonian cycle problem is NP-Complete

B. If $G$ is an undirected Bipartite graph with an odd number of vertices, then $G$ is Hamiltonian.

C. Hamiltonian path problem cannot be solved in polynomial time on directed acyclic graph

D. If $G$ is a connected undirected graph with at least three vertices and $G^3$ is the graph obtained by connecting all pairs of vertices that are connected by a path in $G$ of length at most $3$.

E. If any NP complete problem is polynomial time solvable the $(P=NP)$.

Choose the most appropriate answer from the options given below: