A Variant of the Hadwiger-Debrunner (p, q)-Problem in the Plane

Govindarajan, Sathish and Nivasch, Gabriel (2015) A Variant of the Hadwiger-Debrunner (p, q)-Problem in the Plane. In: DISCRETE & COMPUTATIONAL GEOMETRY, 54 (3). pp. 637-646.

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Abstract

Let X be a convex curve in the plane (say, the unit circle), and let be a family of planar convex bodies such that every two of them meet at a point of X. Then has a transversal of size at most . Suppose instead that only satisfies the following ``(p, 2)-condition'': Among every p elements of , there are two that meet at a common point of X. Then has a transversal of size . For comparison, the best known bound for the Hadwiger-Debrunner (p, q)-problem in the plane, with , is . Our result generalizes appropriately for if is, for example, the moment curve.

Item Type:	Journal Article
Publication:	DISCRETE & COMPUTATIONAL GEOMETRY
Publisher:	SPRINGER
Additional Information:	Copy right for this article belongs to the SPRINGER, 233 SPRING ST, NEW YORK, NY 10013 USA
Keywords:	Convex set; Transversal; Hadwiger-Debrunner (p, q)-problem; Weak epsilon-net; Helly's theorem; Fractional Helly
Department/Centre:	Division of Electrical Sciences > Computer Science & Automation
Date Deposited:	01 Oct 2015 04:27
Last Modified:	01 Oct 2015 04:27
URI:	http://eprints.iisc.ac.in/id/eprint/52469

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