NOT b) = TRUE. In contrast, "a AND NOT a" is unsatisfiable. Like 3SAT, PLANAR-SAT is NP-complete, and is commonly used in reductions. Every 3SAT problem...

Satisfiability modulo theories Counting SAT Planar SAT Karloff–Zwick algorithm Circuit satisfiability The SAT problem for arbitrary formulas is NP-complete...

Boolean circuit whose underlying graph is planar) containing only NAND gates with exactly two inputs. Planar Circuit SAT is the decision problem of determining...

characterizing which SAT-like problems are #P-complete. This is the counting version of Planar 3SAT. The hardness reduction from 3SAT to Planar 3SAT given by...

classifications) provided in an expository paper by Hubie Chen. Planar TQBF, generalizing Planar SAT, was proved PSPACE-complete by D. Lichtenstein. M. Garey...

In computer science, 2-satisfiability, 2-SAT or just 2SAT is a computational problem of assigning values to variables, each of which has two possible...

and dominating set problems for planar graphs are NP-complete, but can be solved in subexponential time using the planar separator theorem. "Each instance...

undirected planar graphs of maximum degree three, directed planar graphs with indegree and outdegree at most two, bridgeless undirected planar 3-regular...

In topological graph theory, a 1-planar graph is a graph that can be drawn in the Euclidean plane in such a way that each edge has at most one crossing...

points), the problem is NP-hard. This can be proved by reduction from Planar SAT. For the case in which all holes are single points, several constant-factor...