Title: Recognizing String Graphs in NP
Published: October 2001
Authors: Marcus Schaefer, Eric SedgwickDaniel Štefankovic
Abstract: A string graph is the intersection graph of a set of curves in the plane. Each curve is represented by a vertex, and an edge between two vertices reflects that the corresponding curves intersect. We show that string graphs can be recognized in NP. The recognition problem was not known to be decidable until very recently, when two independent papers established exponential upper bounds on the number of intersections needed to realize a string graph (Pach, Toth, and Schaefer, Stefankovic, 2001). These results implied that the recognition problem lies in NEXP. In the present paper we improve this by showing that the recognition problem for string graphs is in NP, and therefore NP-complete, since Kratochvil showed in 1991 that the recognition problem is NP-hard. The result has consequences for the computational complexity of problems in graph drawing, and topological inference.
Full Paper: [postscript]