### Abstract

In a witness rectangle graph (WRG) on vertex point set P with respect to witness point set W in the plane, two points x,y in P are adjacent whenever the open rectangle with x and y as opposite corners contains at least one point in W. WRGs are representative of a larger family of witness proximity graphs introduced in two previous papers. We study graph-theoretic properties of WRGs. We prove that any WRG has at most two non-trivial connected components. We bound the diameter of the non-trivial connected components of a WRG in both the one-component and two-component cases. In the latter case, we prove that a graph is representable as a WRG if and only if each component is a co-interval graph, thereby providing a complete characterization of WRGs of this type. We also completely characterize trees drawable as WRGs. Finally, we conclude with some related results on the number of points required to stab all the rectangles defined by a set of n points.

Original language | English (US) |
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Title of host publication | Algorithms and Data Structures - 12th International Symposium, WADS 2011, Proceedings |

Pages | 73-85 |

Number of pages | 13 |

DOIs | |

State | Published - 2011 |

Event | 12th International Symposium on Algorithms and Data Structures, WADS 2011 - New York, NY, United States Duration: Aug 15 2011 → Aug 17 2011 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 6844 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 12th International Symposium on Algorithms and Data Structures, WADS 2011 |
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Country | United States |

City | New York, NY |

Period | 8/15/11 → 8/17/11 |

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

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## Cite this

*Algorithms and Data Structures - 12th International Symposium, WADS 2011, Proceedings*(pp. 73-85). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 6844 LNCS). https://doi.org/10.1007/978-3-642-22300-6_7