Noncrossing subgraphs in topological layouts
SIAM Journal on Discrete Mathematics
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
Crossing Numbers of Graphs, Lower Bound Techniques
GD '94 Proceedings of the DIMACS International Workshop on Graph Drawing
Algorithmic Graph Theory and Perfect Graphs (Annals of Discrete Mathematics, Vol 57)
Algorithmic Graph Theory and Perfect Graphs (Annals of Discrete Mathematics, Vol 57)
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Recognizing string graphs in NP
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Layered Drawings of Graphs with Crossing Constraints
COCOON '01 Proceedings of the 7th Annual International Conference on Computing and Combinatorics
Recognizing string graphs in NP
Journal of Computer and System Sciences - STOC 2002
Journal of Computer and System Sciences - STOC 2001
Simultaneous graph embeddings with fixed edges
WG'06 Proceedings of the 32nd international conference on Graph-Theoretic Concepts in Computer Science
Crossing-constrained hierarchical drawings
Journal of Discrete Algorithms
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We revoke the problem of drawing graphs in the plane so that only certain specified pairs of edges are allowed to cross. We overview some previous results and open problems, namely the connection to intersection graphs of curves in the plane. We complement these by stating a new conjecture and showing that its proof would solve the problem of algorithmic decidability of recognition of string graphs as well as realizability of abstract topological graphs and feasible drawability of graphs with restricted edge crossings.