Combinatorial map

A combinatorial map is a combinatorial object modelling topological structures with subdivided objects. Historically, the concept was introduced informally by J. Edmonds for polyhedral surfaces which are planar graphs. It was given its first definite formal expression under the name "Constellations" by A. Jacques but the concept was already extensively used under the name "rotation" by Gerhard Ringel and J.W.T. Youngs in their famous solution of the Heawood map-coloring problem. The term "constellation" was not retained and instead "combinatorial map" was favored. The concept was later extended to represent higher-dimensional orientable subdivided objects. Combinatorial maps are used as efficient data structures in image representation and processing, in geometrical modeling. This model is related to simplicial complexes and to combinatorial topology. Note that combinatorial maps were extended to generalized maps that allow also to represent non-orientable objects like the Möbius strip and the Klein bottle. A combinatorial map is a boundary representation model; it represents object by its boundaries.