Two approaches for hamiltonian circuit problem using satisfiability

Abstract

A Hamiltonian circuit is a cycle in a graph which visits each vertex exactly once and also returns to the starting vertex. Determining whether such cycles exist in graphs is the Hamiltonian Circuit problem. In this paper, we propose two different approaches to solve the problem. Both our approaches proceed, by reducing a given graph to its equivalent 3-SAT representation. Further, we explore the generated clauses to determine a satisfying truth value assignment. If the values assigned evaluate the clauses to true it indicates the presence of Hamiltonian circuit otherwise not. The two approaches differ in the number of constraints used for reduction. The approach discussed, is better than the already existing backtracking and heuristic based approaches.