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arXiv · 1407.0642

About an Erdős-Grünbaum conjecture concerning piercing of non bounded convex sets

Amanda Montejano·Luis Montejano·Edgardo Roldán-Pensado·Pablo Soberón
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Abstract

In this paper, we study the number of compact sets needed in an infinite family of convex sets with a local intersection structure to imply a bound on its piercing number, answering a conjecture of Erdős and Grünbaum. Namely, if in an infinite family of convex sets in $\mathbb{R}^d$ we know that out of every $p$ there are $q$ which are intersecting, we determine if having some compact sets implies a bound on the number of points needed to intersect the whole family. We also study variations of this problem.

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Amanda Montejano, Luis Montejano, Edgardo Roldán-Pensado, Pablo Soberón. 2014-12-24. About an Erdős-Grünbaum conjecture concerning piercing of non bounded convex sets. https://arxiv.org/abs/1407.0642

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