GD 2005: Graph Drawing pp 61-72

# On Rectilinear Duals for Vertex-Weighted Plane Graphs

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

## 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.

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