I'm trying to prove that if all vertices of a finite undirected graph are of odd degree, then each edge is contained within an even number of Hamiltonian cycles. (or none).
I know a Hamiltonian cycle in a graph is every cycle that contains each vertex in the graph exactly once. I tried to prove the problem by using geometrical figures with some extra edges added but it didn't work out. I would be really thankful if someone could explain their solution to this problem!