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embeddings on non-compact surfaces (the Euclidean plane!) are definitely considered |
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* no arcs include points associated with other vertices,
* two arcs never intersect at a point which is interior to either of the arcs.
Here a surface is a
Informally, an embedding of a graph into a surface is a drawing of the graph on the surface in such a way that its edges may intersect only at their endpoints. It is well known that any finite graph can be embedded in 3-dimensional Euclidean space <math>\mathbb{R}^3</math>.<ref name="3d-gd">{{citation
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