True/False: Let G be a connected undirected graph such that all vertices have even degrees. Every Euler cycle in G is also a Hamiltonian cycle if and only if G is a cycle graph.
I think this one is true, I can see that if I draw a simple Cycle graph, but I have no clue on how to prove it.
I know Ore's and Dirac's theorems, but they only work for a small n.
Any help will be appreciated!
Thank you!