Designing SAT for HCP

Details Designing SAT for HCP Designing SAT for HCP

1999-03-05

arxiv.org/abs/cs/9903006v1

Computer Science

Logic in Computer Science

7 pages, 1 figures. It has sent to 6th Twente Workshop on Graphs and Combinatorial Optimization

Scientific paper

For arbitrary undirected graph $G$, we are designing SATISFIABILITY problem (SAT) for HCP, using tools of Boolean algebra only. The obtained SAT be the logic formulation of conditions for Hamiltonian cycle existence, and use $m$ Boolean variables, where $m$ is the number of graph edges. This Boolean expression is true if and only if an initial graph is Hamiltonian. That is, each satisfying assignment of the Boolean variables determines a Hamiltonian cycle of $G$, and each Hamiltonian cycle of $G$ corresponds to a satisfying assignment of the Boolean variables. In common case, the obtained Boolean expression may has an exponential length (the number of Boolean literals).

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