### Abstract

For k>0 let f(k) denote the minimum integer f such that, for any family of k pairwise disjoint congruent disks in the plane, there is a direction α such that any line having direction α intersects at most f of the disks. We determine the exact asymptotic behavior of f(k) by proving that there are two positive constants d_{1}, d_{2} such that d_{1}√k √log k≤f(k)≤d_{2}√k √log k. This result has been motivated by problems dealing with the separation of convex sets by straight lines.

Original language | English (US) |
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Pages (from-to) | 239-243 |

Number of pages | 5 |

Journal | Discrete & Computational Geometry |

Volume | 4 |

Issue number | 1 |

DOIs | |

State | Published - Dec 1 1989 |

Externally published | Yes |

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Discrete Mathematics and Combinatorics
- Geometry and Topology
- Computational Theory and Mathematics

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## Cite this

Alon, N., Katchalski, M., & Pulleyblank, W. R. (1989). Cutting disjoint disks by straight lines.

*Discrete & Computational Geometry*,*4*(1), 239-243. https://doi.org/10.1007/BF02187724