## Abstract

We study the following local-to-global phenomenon: Let

Minkowski arrangements.

*B*and*R*be two finite sets of (blue and red) points in the Euclidean plane R^{2}. Suppose that in each “neighborhood” of a red point, the number of blue points is at least as large as the number of red points. We show that in this case the total number of blue points is at least one fifth of the total number of red points. We also show that this bound is optimal and we generalize the result to arbitrary dimension and arbitrary norm using results fromMinkowski arrangements.

Original language | English GB |
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Publisher | arXiv:1701.02200 [cs.CG] |

State | Published - 20 Apr 2017 |

## Keywords

- Computer Science - Computational Geometry