On Rectilinear Duals for Vertex-Weighted Plane Graphs
De Berg, Mark and Mumford, Elena and Speckmann, Bettina (2006) On Rectilinear Duals for Vertex-Weighted Plane Graphs. In: Graph Drawing 13th International Symposium, GD 2005, September 12-14, 2005, Limerick, Ireland , pp. 61-72 (Official URL: http://dx.doi.org/10.1007/11618058_6).
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Let G = (V,E) be a plane triangulated graph where each vertex is assigned a positive weight. A rectilinear dual of 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 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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