I found out that "No solution exists to get HC in polynomial time and there are no such conditions to decide the probability of HC exists (Neapolitan and Naimipour, 1996)." But also Bellman-Ford algorithm is a polynomial-time algorithm. Therefore, I guess this question is False?
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The Bellman–Ford algorithm is for the shortest path problem, not the Hamiltonian path problem. see e.g. https://math.stackexchange.com/questions/3970279/using-bellman-ford-to-find-a-hamiltonian-cycle-np-complete – Thomas Lesgourgues Nov 23 '21 at 21:33
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What is HC? Is it "Hamiltonian circuit"? I didn't check the reference but I highly doubt that the authors write that it cannot be found in polynomial time, since the question of whether there is such an algorithm is one of the most important open questions in contemporary mathematics. – Dániel Garamvölgyi Nov 26 '21 at 10:48