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

## TL;DR

This paper introduces SFCM-R, a new algorithm designed to address the NP-Complete Hamiltonian sequence problem by degenerating potential forbidden minors through a two-phase process.

## Contribution

The paper presents a novel algorithm that approaches the Hamiltonian sequence problem by degenerating forbidden minors, offering a new method for tackling this NP-Complete challenge.

## Key findings

- Algorithm successfully degenerates potential forbidden minors.
- Constructs and reconstructs potential Hamiltonian sequences.
- Provides a new approach to NP-Complete Hamiltonian problems.

## Abstract

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