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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de Berg, M., Mumford, E., Speckmann, B. (2006). On Rectilinear Duals for Vertex-Weighted Plane Graphs. In: Healy, P., Nikolov, N.S. (eds) Graph Drawing. GD 2005. Lecture Notes in Computer Science, vol 3843. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11618058_6
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DOI: https://doi.org/10.1007/11618058_6
Publisher Name: Springer, Berlin, Heidelberg
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