Abstrakt
In a rectilinear dual of a planar graph vertices are represented by sim- ple rectilinear polygons, while edges are represented by side-contact between the corresponding polygons. A rectilinear dual is called a cartogram if the area of each region is equal to a pre-specified weight.
The complexity of a cartogram is determined by the maximum number of corners (or sides) required for any polygon. In a series of papers the polygonal complexity of such representations for maximal planar graphs has been reduced from the initial 40 to 34, then to 12 and very recently to the currently best known 10.
Here we describe a construction with 8-sided polygons, which is opti- mal in terms of polygonal complexity as 8-sided polygons are sometimes necessary.