String graphs. I.: the number of critical nonstring graphs is infinite
Journal of Combinatorial Theory Series B
String graphs. II.: Recognizing string graphs is NP-hard
Journal of Combinatorial Theory Series B
String graphs requiring exponential representations
Journal of Combinatorial Theory Series B
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Which crossing number is it anyway?
Journal of Combinatorial Theory Series B
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Efficient Algorithms for Lempel-Zip Encoding (Extended Abstract)
SWAT '96 Proceedings of the 5th Scandinavian Workshop on Algorithm Theory
Solving Trace Equations Using Lexicographical Normal Forms
ICALP '97 Proceedings of the 24th International Colloquium on Automata, Languages and Programming
Application of Lempel-Ziv Encodings to the Solution of Words Equations
ICALP '98 Proceedings of the 25th International Colloquium on Automata, Languages and Programming
Crossing Number of Abstract Topological Graphs
GD '98 Proceedings of the 6th International Symposium on Graph Drawing
Recognizing String Graphs Is Decidable
GD '01 Revised Papers from the 9th International Symposium on Graph Drawing
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
IJCAI'95 Proceedings of the 14th international joint conference on Artificial intelligence - Volume 1
Journal of the ACM (JACM)
Algorithms for Normal Curves and Surfaces
COCOON '02 Proceedings of the 8th Annual International Conference on Computing and Combinatorics
Satisfiability of word equations with constants is in PSPACE
Journal of the ACM (JACM)
A remark about quadratic trace equations
DLT'02 Proceedings of the 6th international conference on Developments in language theory
Can they cross? and how?: (the hitchhiker's guide to the universe of geometric intersection graphs)
Proceedings of the twenty-seventh annual symposium on Computational geometry
Computing the independence number of intersection graphs
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Geometric intersection graph: do short cycles help?
COCOON'07 Proceedings of the 13th annual international conference on Computing and Combinatorics
Extending partial representations of function graphs and permutation graphs
ESA'12 Proceedings of the 20th Annual European conference on Algorithms
Crossing-constrained hierarchical drawings
Journal of Discrete Algorithms
Hi-index | 0.00 |
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 [18, 20]. 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 Kratochvíl [12] showed that the recognition problem is NP-hard. The result has consequences for the computational complexity of problems in graph drawing, and topological inference.