Hamiltonian Cycle Problem
Given an undirected graph, find a tour that visits each vertex exactly once, or determine no tour exists.
Hamiltonian Path Problem
Here, we want a path instead of a cycle, where the start is not the end. This problem is hard.
Rudrata’s Problem
This is a specific case of a Hamiltonian tour where you are looking for a knight’s tour on a chess board trying to find a way that each square can be visited once.