Prove if this statement is true: every graph consisting of two edge-disjoint Hamiltonian paths contains a Hamiltonian cycle.
Two edge-disjoint Hamiltonian paths means all vertices can be connected with two different paths of no edges in common; so the graph has at least 2(n-1) edges in total if the graph has n vertices. I am not sure how to relate this to hamilton cycle (how to add one more edge to the path to make it a cycle.)