A special planar satisfiability problem and a consequence of its NP-completeness
Discrete Applied Mathematics
A Computing Procedure for Quantification Theory
Journal of the ACM (JACM)
The complexity of theorem-proving procedures
STOC '71 Proceedings of the third annual ACM symposium on Theory of computing
Polynomial algorithm for finding the largest independent sets in graphs without forks
Discrete Applied Mathematics
Boundary properties of graphs for algorithmic graph problems
Theoretical Computer Science
Satisfiability of acyclic and almost acyclic CNF formulas (II)
SAT'11 Proceedings of the 14th international conference on Theory and application of satisfiability testing
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The satisfiability problem is known to be NP-complete in general and for many restricted instances, such as CNF formulas with at most 3 variables per clause and at most 3 occurrences per variable, or planar formulas. The latter example refers to graphs representing satisfiability instances. These are bipartite graphs with vertices representing clauses and variables, and edges connecting variables to the clauses containing them. Finding the strongest possible restrictions under which the problem remains NP-complete is important for at least two reasons. First, this can make it easier to establish the NP-completeness of new problems by allowing easier transformations. Second, this can help clarify the boundary between tractable and intractable instances of the problem. In this paper, we address the second issue and reveal the first boundary property of graphs representing satisfiability instances.