Journal of Algorithms
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Polychromatic colorings of plane graphs
Proceedings of the twenty-fourth annual symposium on Computational geometry
On the complexity of planar covering of small graphs
WG'11 Proceedings of the 37th international conference on Graph-Theoretic Concepts in Computer Science
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Lichtenstein proposed the use of a "planar" version of 3SAT as a departure point for proofs of NP -completeness that would at once prove the general graph problem as well as its restriction to planar graphs to be NP-complete. Dyer and Frieze later proved that Planar lin3SAT is also NP-complete. Of the three standard versions of 3SAT, only NAE3SAT remained open. We provide a very simple reduction from NAE3SAT to Simple MaxCut, which respects Lichtenstein's conditions; since it is known that the planar version of (Simple) MaxCut is in P, so is the planar version of NAE3SAT, thereby setting the question (if in a somewhat unexpected way).