Decidability of string graphs

@inproceedings{Schaefer2001DecidabilityOS,
  title={Decidability of string graphs},
  author={M. Schaefer and Daniel Stefankovic},
  booktitle={STOC '01},
  year={2001}
}
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 drawing realizing the string graph in the plane. This upper bound confirms a conjecture by Kratochv\'{\i}l and Matou\v{s}ek~\cite{KM91} and settles the long-standing open problem of the decidability of string graph recognition (Sinden~\cite{S66}, Graham~\cite{G76}). Finally we show how to apply the result to solve another old open problem… Expand
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