## Abstract

We show the following discrete Helly-type results in the plane. Let P be a set of points and D a family of convex pseudodisks in the plane s.t. every triple of pseudodisks in D intersects at a point in P. Then, two of the points in P hit all pseudodisks in D. Three similar results that we prove with the roles of points and regions exchanged are the following: let P be a set of points and H a set of halfspaces in the plane s.t. every triple of points from P is covered by some halfspace in H. Then, two of the halfspaces in H cover all points in P. If, instead, every pair of points in P is covered by some halfspace in H, we show that three of halfspaces in H suffice to cover all points in P. Finally, we show that if every pair of points is covered by an axis-parallel rectangle, then five rectangles are required to cover all points.

Original language | English (US) |
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Pages | 332-335 |

Number of pages | 4 |

State | Published - 2020 |

Event | 32nd Canadian Conference on Computational Geometry, CCCG 2020 - Saskatoon, Canada Duration: Aug 5 2020 → Aug 7 2020 |

### Conference

Conference | 32nd Canadian Conference on Computational Geometry, CCCG 2020 |
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Country/Territory | Canada |

City | Saskatoon |

Period | 8/5/20 → 8/7/20 |

## ASJC Scopus subject areas

- Geometry and Topology
- Computational Mathematics