Combinatorial map

It has been suggested that Map (graph theory) be merged into this article. (Discuss) Proposed since September 2024.

It has been suggested that Rotation system be merged into this article. (Discuss) Proposed since September 2024.

A combinatorial map is a combinatorial representation of a graph on an orientable surface. A combinatorial map may also be called a combinatorial embedding, a rotation system, an orientable ribbon graph, a fat graph, or a cyclic graph.^[1] More generally, an ${\displaystyle n}$-dimensional combinatorial map is a combinatorial representation of a graph on an ${\displaystyle n}$-dimensional orientable manifold.

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. A combinatorial map is a boundary representation model; it represents object by its boundaries.