If we have an undirected graph, is the existence of a Hamiltonian cycle in the graph equivalent to finding a subset of edges S in the graph such that every vertice appears in exactly two different edges in S?
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What happens if the graph is not connected?
Mark Bennet
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@Magdiragdag I can see your point, but as it stands the question needs some attention before it deserves a full answer. What I have put is an attempt to get OP to think about the situation, without doing too much. – Mark Bennet Dec 22 '17 at 03:05