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A Family of Convex Sets in the Plane Satisfying the (4, 3)-Property can be Pierced by Nine Points

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Abstract

We prove that every finite family of convex sets in the plane satisfying the (4, 3)-property can be pierced by nine points. This improves the bound of 13 proved by Kleitman et al. (Combinatorica 21(2), 221–232 (2001)).

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Acknowledgements

The author would like to thank Shira Zerbib for many helpful remarks and for improving the overall presentation of this paper. The author would also like to thank the anonymous referees. Their comments led to improved notation and overall readability of this paper, including a simpler proof of Lemma 3.4.

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  1. 396 Carver Hall, Ames, IA, 50011, USA

    Daniel McGinnis

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  1. Daniel McGinnis
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Correspondence to Daniel McGinnis.

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The author was supported by NSF Grant DMS-1839918 (RTG).

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McGinnis, D. A Family of Convex Sets in the Plane Satisfying the (4, 3)-Property can be Pierced by Nine Points. Discrete Comput Geom 68, 860–880 (2022). https://doi.org/10.1007/s00454-022-00391-y

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  • DOI: https://doi.org/10.1007/s00454-022-00391-y

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