Designing SAT for HCP

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).