# Combinatorial embedding of a graph

Here : http://www.planarity.org/Klein_elementary_graph_theory.pdf (in chapter embeddings) is given definition of combinatorial embedding of a planar graph. (with definition of faces and so on) Though it could be easily used for any graph, they define planar graph as the graph, for which Euler formula holds (assuming that graph is connected). It pretty much understandable that for every plane graph the definition of faces in combinatorial embedding is similar to the definition of faces in topological embedding. (assuming that graph is connected. Otherwise in combinatorial embedding we'll have infinite face for every connected component)

The question is: if for some connected graph it's combinatorial embedding satisfies Euler formula, does this mean that this graph is planar in topological sense (it has plane embedding, i.e. it's plane graph)?

• Later in this paper they give an answer that this is possible. But can anyone give some links to the proof? – Finsky Sep 14 '12 at 6:43