Question: Let G be an undirected graph with weighted edges. A heavy Hamiltonian path is a path P that passes through each vertex of G exactly

Let G be an undirected graph with weighted edges. A heavy Hamiltonian path is a path P that passes through each vertex of G exactly once, such that the total weight of the edges in P is at least half of the total weight of all edges in G. Prove that deciding if a graph has a heavy Hamiltonian path is NP-complete.

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