Touching graphs of unit balls

  • Petr Hliněný
Packing, Compressing, and Touching
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1353)

Abstract

The touching graph of balls is a graph that admits a representation by non-intersecting balls in the space (of prescribed dimension), so that its edges correspond to touching pairs of balls. By a classical result of Koebe [5], the disc touching graphs are exactly the planar graphs. This paper deals with a recognition of unit-ball touching graphs. The 2-dimensional case was proved to be NP-hard by Breu and Kirkpatrick [1]. We show in this paper that also unit-ball touching graphs in dimensions 3 and 4 are NP-hard to recognize. By a recent result of Kirkpatrick and Rote, these results may be transferred in ball-touching graphs in one dimension higher.

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Copyright information

© Springer-Verlag 1997

Authors and Affiliations

  • Petr Hliněný
    • 1
  1. 1.Dept. of Applied MathematicsCharles UniversityPraha 1

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