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A hamiltonian sequence is a path walk $P$ that can be a hamiltonian path orhamiltonian circuit. Determining whether such hamiltonian sequence exists in agiven graph \G is a NP-Complete problem. In this paper, a novel algorithm forhamiltonian sequence problem is proposed. The proposed algorithm assumes that$G$ has potential forbidden minors that prevent a potential hamiltoniansequence $P^\prime$ from being a hamiltonian sequence. The algorithm's goal isto degenerate such potential forbidden minors in a two-phrase process. In firstphrase, the algorithm passes through $G$ in order to construct a potentialhamiltonian sequence $P^\prime$ with the aim of degenerating these potentialforbidden minors. The algorithm, in turn, tries to reconstruct $P^\prime$ insecond phrase by using a goal-oriented approach.

SFCM-R: A novel algorithm for the hamiltonian sequence problem