How to efficiently find all Hamiltonian paths in an undirected graph, withou just using DFS?

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I have problem where i need to display all nodes which are included in a path(from source to destination), but in such a way that we visit every node in the path only once. Solution with only DFS (and marking visited elements) is not fast enough. Someone told me to use articulation points, but i do not see how to do that. Can you help me?

Thanks.

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