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arXiv · 2207.14368

Colorful two-piercing theorem for boxes

Sourav Chakraborty·Arijit Ghosh·Soumi Nandi
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Abstract

We prove a colorful extension of a Helly-type theorem by Danzer and Gr\"{u}nbaum (Combinatorica, 1982) concerning two-piercing families of axis-parallel boxes in $\mathbb{R}^d$. We also show that our result is tight by constructing extremal families that achieve the bound. Related work includes a graph-theoretic proof of the original theorem by Pendavingh, Puite, and Woeginger (Discrete Applied Mathematics, 2008), and a two-piercing result for lower-dimensional boxes by Ba\~{n}os and Oliveros (Acta Mathematica Hungarica, 2018).

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Sourav Chakraborty, Arijit Ghosh, Soumi Nandi. 2022-07-28. Colorful two-piercing theorem for boxes. https://doi.org/10.1016/j.dam.2025.11.044

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