J. Kratochvil, A SPECIAL PLANAR SATISFIABILITY PROBLEM AND A CONSEQUENCE OF ITS NP-COMPLETENESS, Discrete applied mathematics, 52(3), 1994, pp. 233-252
We introduce a weaker but still NP-complete satisfiability problem to
prove NP-completeness of recognizing several classes of intersection g
raphs of geometric objects in the plane, including grid intersection g
raphs and graphs of boxicity two.