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An algorithm is given for finding the solutions to 3SAT problems. Thealgorithm uses Bienstock's reduction from 3SAT to existence of induced oddcycle of length greater than three, passing through a prescribed node in theconstructed graph. The algorithm proceeds to find what will be called the holecomplexes of the graph. The set of the boundary nodes of the hole complexcontaining the prescribed node is then searched for the subsets of 8 nodescorresponding to the 3SAT's literals. If a complete set of literals iscontained in the boundary then the 3SAT is solvable.

Solving 3SAT By Reduction To Testing For Odd Hole