I have a question, and also an answer which I assume, is correct, but would like to ask, if some of you could elaborate, and add validity to the provided claim or develop a discussion.
I did not find this question, nor the answer anywhere.
Is there any formal association or fundamental relationship, (as in some kind of theorem etc.) between Hamiltonian graphs and Eulerian graphs?
No such thing exist. Simple proof is, that finding a Hamiltonian path in a graph is NP-hard problem, and finding Eulerian path is not a NP-hard problem. Or in other words: If this statement is indeed true, finding the Eulerian path should also be NP-hard problem, which we know is not.