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Discrete & Computational Geometry

, Volume 28, Issue 4, pp 649–670 | Cite as

Independence Numbers of Planar Contact Graphs

  • Swanepoel
Article

Abstract

We show that for a large class of convex discs C (including strictly convex discs), there exists an ε=ε(C)>0 such that the independence number of the contact graph of any packing of n translates of C in the plane is at least (1/4 + ε)n . For C a circle, we improve the lower bound of Csizmadia to 8/31n.

Copyright information

© Springer-Verlag New York Inc. 2002

Authors and Affiliations

  • Swanepoel
    • 1
  1. 1.Department of Mathematics, Applied Mathematics and Astronomy, University of South Africa, PO Box 392, Unisa 0003, South Africa swanekj@unisa.ac.zaSouth Africa

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