#Looking for theorems or lemma about SHP's (shortest hamiltonian path's) first and last vertices
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Have you tried Google OR-Tools? It handles TSP variants including fixed start/end points really well. 👀
no, I'm looking for a general answer and not fixed start/end points, but given a graph (if hamiltonian), where could be starting/ending points?
For Hamiltonian paths, try testing peripheral/leaf nodes as endpoints first, or nodes with degree 1-2. If the graph has specific structure, endpoints are often at the ‘edges’ of the graph.
(Sorry, excuse me for the response time, my cat lost me)
the graph is complete and weights are any real numbers
I'm not looking for "good" solution but exact one