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Geometric Thickness of Complete Graphs

  • Michael B. Dillencourt
  • David Eppstein
  • DanielS. Hirschberg
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1547)

Abstract

We define the geometric thickness of a graph to be the smallest number of layers such that we can draw the graph in the plane with straight-line edges and assign each edge to a layer so that no two edges on the same layer cross. The geometric thickness lies between two previously studied quantities, the (graph-theoretical) thickness and the book thickness. We investigate the geometric thickness of the family of complete graphs, K n . We show that the geometric thickness of K n lies between ⌈(n/5.646) +0.342⌉ and ⌈n/4⌉, and we give exact values of the geometric thickness of K n for n ≤ 12 and n ∈ 15,16.

Keywords

Convex Hull Complete Graph Outer Ring Layer Cross Planar Embedding 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Michael B. Dillencourt
    • 1
  • David Eppstein
    • 1
  • DanielS. Hirschberg
    • 1
  1. 1.Information and Computer ScienceUniversity of CaliforniaIrvineUSA

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