## Abstract

Unit disk graphs are the intersection graphs of equal sized circles in the plane: they provide a graph-theoretic model for broadcast networks (cellular networks) and for some problems in computational geometry. We show that many standard graph theoretic problems remain NP-complete on unit disk graphs, including coloring, independent set, domination, independent domination, and connected domination; NP-completeness for the domination problem is shown to hold even for grid graphs, a subclass of unit disk graphs. In contrast, we give a polynomial time algorithm for finding cliques when the geometric representation (circles in the plane) is provided.

Original language | English (US) |
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Pages (from-to) | 165-177 |

Number of pages | 13 |

Journal | Discrete Mathematics |

Volume | 86 |

Issue number | 1-3 |

DOIs | |

State | Published - Dec 14 1990 |

Externally published | Yes |

## ASJC Scopus subject areas

- Theoretical Computer Science
- Discrete Mathematics and Combinatorics