## Abstract

Suppose we are given a set D of n pairwise intersecting disks in the plane. A planar point set P stabs D if and only if each disk in D contains at least one point from P. We present a deterministic algorithm that takes O(n) time to find five points that stab D. Furthermore, we give a simple example of 13 pairwise intersecting disks that cannot be stabbed by three points. Moreover, we present a simple argument showing that eight disks can be stabbed by at most three points. This provides a simple – albeit slightly weaker – algorithmic version of a classical result by Danzer that such a set D can always be stabbed by four points.

Original language | English |
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Article number | 112403 |

Journal | Discrete Mathematics |

Volume | 344 |

Issue number | 7 |

DOIs | |

State | Published - Jul 2021 |

## Keywords

- Disk intersection graph
- LP-type problem
- Stabbing set