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Compact encodings of the connectivity of planar triangulations is a very important subject not only in graph theory but also in computer graphics. For triangle meshes used in computer graphics the topologically planar regions dominate by far. New results by Isenburg et al. [6] even show that the connectivity is sufficient to describe shape by itself. Most coding methods for planar triangulations can be extended to manifolds of bounded genus with the same upper and lower bounds on the bit rate.

Connectivity Coding: New Perspectives for Mesh Compression (Connectivity Coding: Neue Perspektiven für die Kompression von Dreiecksnetzen)