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STOC
2002
ACM

Recognizing string graphs in NP

15 years 7 days ago
Recognizing string graphs in NP
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 means 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 (Mutzel (Ed.), Graph Drawing 2001, Lecture Notes in Computer Science, Springer, Berlin; Proceedings of the 33rd Annual ACM Symposium on Theory of Computing (STOC-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 Kratochvi?l showed that the recognition problem is NP-hard (J. Combin Theory, Ser. B 52). The result has consequences for the computational complexity of problems in graph drawi...
Marcus Schaefer, Eric Sedgwick, Daniel Stefankovic
Added 03 Dec 2009
Updated 03 Dec 2009
Type Conference
Year 2002
Where STOC
Authors Marcus Schaefer, Eric Sedgwick, Daniel Stefankovic
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