ePrints@IIScePrints@IISc Home | About | Browse | Latest Additions | Advanced Search | Contact | Help

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.

[img] PDF
Dis_Com_Geo_54-3_ 637_2015.pdf - Published Version
Restricted to Registered users only

Download (445kB) | Request a copy
Official URL: http://dx.doi.org/10.1007/s00454-015-9723-9

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
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
Depositing User: Id for Latest eprints
Date Deposited: 01 Oct 2015 04:27
Last Modified: 01 Oct 2015 04:27
URI: http://eprints.iisc.ac.in/id/eprint/52469

Actions (login required)

View Item View Item