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
Topological queries in spatial databases
Journal of Computer and System Sciences
Embedding planar graphs on the grid
SODA '90 Proceedings of the first annual ACM-SIAM symposium on Discrete algorithms
Maintaining knowledge about temporal intervals
Communications of the ACM
Which crossing number is it anyway?
Journal of Combinatorial Theory Series B
Computing crossing numbers in quadratic time
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
DIAGRAMS '02 Proceedings of the Second International Conference on Diagrammatic Representation and Inference
Reasoning about Binary Topological Relations
SSD '91 Proceedings of the Second International Symposium on Advances in Spatial Databases
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
Linear-Time Recognition of Circular-Arc Graphs
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
IJCAI'95 Proceedings of the 14th international joint conference on Artificial intelligence - Volume 1
The complexity of several realizability problems for abstract topological graphs
GD'07 Proceedings of the 15th international conference on Graph drawing
Blocks of hypergraphs: applied to hypergraphs and outerplanarity
IWOCA'10 Proceedings of the 21st international conference on Combinatorial algorithms
Formalization and reasoning about spatial semantic integrity constraints
Data & Knowledge Engineering
Shortest non-crossing walks in the plane
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Complexity of some geometric and topological problems
GD'09 Proceedings of the 17th international conference on Graph Drawing
String graphs and incomparability graphs
Proceedings of the twenty-eighth annual symposium on Computational geometry
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We show that string graphs can be recognized in nondeterministic exponential time by giving an exponential upper bound on the number of intersections for a minimal drawing realizing a string graph in the plane. This upper bound confirms a conjecture by Kratochvíl and Matousek (J. Combin. Theory. Ser. B 53 (1991).) and settles the long-standing open problem of the decidability of string graph recognition (Bell System Tech. J. 45 (1996) 1639; Open Problem at Fifth Hungarian Collogium on Combinatories, 1976). Finally we show how to apply the result to solve another old open problem: deciding the existence of Euler diagrams, a fundamental problem of topological inference (Proceedings of the 14th International Joint Conference on Artificial Intelligence, 1995, p. 901). The general theory of Euler diagrams turns out to be as hard as second-order arithmetic.