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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The authors wish to acknowledge the support of CONACYT under project 166306 and support of PAPITT-UNAM under projects IN112614 and IA102013.
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Montejano, A., Montejano, L., Roldán-Pensado, E. et al. About an Erdős–Grünbaum Conjecture Concerning Piercing of Non-bounded Convex Sets. Discrete Comput Geom 53, 941–950 (2015). https://doi.org/10.1007/s00454-015-9664-3
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DOI: https://doi.org/10.1007/s00454-015-9664-3