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
Partial commutation and traces
Handbook of formal languages, vol. 3
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
Applied Combinatorics on Words (Encyclopedia of Mathematics and its Applications)
Applied Combinatorics on Words (Encyclopedia of Mathematics and its Applications)
IJCAI'95 Proceedings of the 14th international joint conference on Artificial intelligence - Volume 1
STACS'99 Proceedings of the 16th annual conference on Theoretical aspects of computer science
A New Approach to Exact Crossing Minimization
ESA '08 Proceedings of the 16th annual European symposium on Algorithms
Journal of Visual Languages and Computing
Spatial reasoning in a fuzzy region connection calculus
Artificial Intelligence
On the Computational Complexity of Spatial Logics with Connectedness Constraints
LPAR '08 Proceedings of the 15th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning
Chordal graphs as intersection graphs of pseudosegments
GD'06 Proceedings of the 14th international conference on Graph drawing
Recognition of polygon-circle graphs and graphs of interval filaments is NP-complete
WG'07 Proceedings of the 33rd international conference on Graph-theoretic concepts in computer science
Customizing qualitative spatial and temporal calculi
AI'07 Proceedings of the 20th Australian joint conference on Advances in artificial intelligence
The complexity of several realizability problems for abstract topological graphs
GD'07 Proceedings of the 15th international conference on Graph drawing
Information Sciences: an International Journal
Simultaneous graph embeddings with fixed edges
WG'06 Proceedings of the 32nd international conference on Graph-Theoretic Concepts in Computer Science
Faithful representations of graphs by islands in the extended grid
LATIN'10 Proceedings of the 9th Latin American conference on Theoretical Informatics
Contact and intersection representations
GD'04 Proceedings of the 12th international conference on Graph Drawing
Train tracks and confluent drawings
GD'04 Proceedings of the 12th international conference on Graph Drawing
Complexity of some geometric and topological problems
GD'09 Proceedings of the 17th international conference on Graph Drawing
Maximum independent set in 2-direction outersegment graphs
WG'11 Proceedings of the 37th international conference on Graph-Theoretic Concepts in Computer Science
Tracing compressed curves in triangulated surfaces
Proceedings of the twenty-eighth annual symposium on Computational geometry
String graphs and incomparability graphs
Proceedings of the twenty-eighth annual symposium on Computational geometry
On the decidability of connectedness constraints in 2D and 3D Euclidean spaces
IJCAI'11 Proceedings of the Twenty-Second international joint conference on Artificial Intelligence - Volume Volume Two
Bend-bounded path intersection graphs: sausages, noodles, and waffles on a grill
WG'12 Proceedings of the 38th international conference on Graph-Theoretic Concepts in Computer Science
Topological Logics with Connectedness over Euclidean Spaces
ACM Transactions on Computational Logic (TOCL)
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 (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 Kratochvíl 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 drawing, and topological inference. We also show that the string graph problem is decidable for surfaces of arbitrary genus.