Intersection Graphs of Noncrossing Arc-Connected Sets in the Plane

@inproceedings{Kratochvl1996IntersectionGO,
  title={Intersection Graphs of Noncrossing Arc-Connected Sets in the Plane},
  author={Jan Kratochv{\'i}l},
  booktitle={Graph Drawing},
  year={1996}
}
Arc-connected sets A, B ⊂E2 are called noncrossing if both A-B and B-A are arc-connected. A graph is called an NCAC graph if it has an intersection representation in which vertices are represented by arc-connected sets in the plane and any two sets of the representation are noncrossing. In particular, disk intersection graphs are NCAC. By a unified reduction we show that recognition of disk intersection and NCAC graphs are NP-hard. A simple observation shows that triangle-free disk intersection… CONTINUE READING

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