### Abstract

Let V be a set of curves in the plane. The corresponding intersection graph has V as the set of vertices, and two vertices are connected by an edge if and only if the two corresponding curves intersect in the plane. It is shown that the set of intersection graphs of curves in the plane is a proper subset of the set of all undirected graphs. Furthermore, the set of intersection graphs of straight line-segments is a proper subset of the set of the intersection graphs of curves in the plane. Finally, it is shown that for every k ≥ 3, the problem of determining whether an intersection graph of straight line-segments is k-colorable is NP-complete.

Original language | English (US) |
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Pages (from-to) | 8-20 |

Number of pages | 13 |

Journal | Journal of Combinatorial Theory, Series B |

Volume | 21 |

Issue number | 1 |

DOIs | |

State | Published - Aug 1976 |

Externally published | Yes |

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Discrete Mathematics and Combinatorics
- Computational Theory and Mathematics

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## Cite this

Ehrlich, G., Even, S., & Tarjan, R. E. (1976). Intersection graphs of curves in the plane.

*Journal of Combinatorial Theory, Series B*,*21*(1), 8-20. https://doi.org/10.1016/0095-8956(76)90022-8