On rectilinear duals for vertex-weighted plane graphs

  • Authors:

  • Mark de Berg;Elena Mumford;Bettina Speckmann

  • Affiliations:

  • Department of Mathematics & Computer Science, TU Eindhoven, The Netherlands;Department of Mathematics & Computer Science, TU Eindhoven, The Netherlands;Department of Mathematics & Computer Science, TU Eindhoven, The Netherlands

  • Venue:
  • GD'05 Proceedings of the 13th international conference on Graph Drawing
  • Year:
  • 2005

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Abstract

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.