Graph embedding: Difference between revisions

Revision as of 20:43, 13 October 2020

Revision as of 21:46, 12 November 2020

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Here a surface is a [[compact space|compact]], [[connected space|connected]] <math>2</math>-[[manifold]].

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

| last1 = Cohen | first1 = Robert F.

| last2 = Eades | first2 = Peter | author2-link = Peter Eades

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| year = 1995| isbn = 978-3-540-58950-1

| doi-access = free

}}.</ref>. A [[planar graph]] is one that can be embedded in 2-dimensional Euclidean space <math>\mathbb{R}^2.</math>

Often, an '''embedding''' is regarded as an equivalence class (under homeomorphisms of <math>\Sigma</math>) of representations of the kind just described.