## Abstract

A point-set S is protecting a collection F = T_{1}, T_{2},...,_{n} of n mutually disjoint compact sets if each one of the sets T_{i} is visible from at least one point in S; thus, for every set T_{i} ∈F there are points x S and yT_{i} such that the line segment joining x to y does not intersect any element in F other than T_{i}. In this paper we prove that [2(n-2)/3] points are always sufficient and occasionally necessary to protect any family F of n mutually disjoint compact convex sets. For an isothetic family F, consisting of n mutually disjoint rectangles, [n/2] points are always sufficient and [n/2] points are sometimes necessary to protect it. If F is a family of triangles, [4 n/7] points are always sufficient. To protect families of n homothetic triangles, [n/2] points are always sufficient and [n/2] points are sometimes necessary.

Original language | English |
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Pages (from-to) | 311-321 |

Number of pages | 11 |

Journal | Graphs and Combinatorics |

Volume | 10 |

Issue number | 2 |

DOIs | |

State | Published - Jun 1994 |

## ASJC Scopus subject areas

- Theoretical Computer Science
- Discrete Mathematics and Combinatorics