On Rectilinear Duals for Vertex-Weighted Plane Graphs

  • Mark de Berg
  • Elena Mumford
  • Bettina Speckmann
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3843)


Let \({\mathcal G}\) = (V,E) be a plane triangulated graph where each vertex is assigned a positive weight. A rectilinear dual of \({\mathcal G}\) is a partition of a rectangle into |V| simple rectilinear regions, one for each vertex, such that two regions are adjacent if and only if the corresponding vertices are connected by an edge in E. A rectilinear dual is called a cartogram if the area of each region is equal to the weight of the corresponding vertex. We show that every vertex-weighted plane triangulated graph \({\mathcal G}\) admits a cartogram of constant complexity, that is, a cartogram where the number of vertices of each region is constant.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Mark de Berg
    • 1
  • Elena Mumford
    • 1
  • Bettina Speckmann
    • 1
  1. 1.Department of Mathematics & Computer ScienceTU EindhovenThe Netherlands

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