TITLE: When is a graph planar?
QUESTION [5 upvotes]: A graph G is planar if and only if xxx.
What can xxx be substituted for? Note that this is from a topological POV so a graph is a 1-dim cw complex and I guess the fundamental group should be used somehow.

REPLY [2 votes]: A very good treatment of when a graph can be embedded in the plane and more generally into other surfaces is given by the excellent book:
Graphs on Surfaces by Bojan Mohar and Carsten Thomassen (John Hopkins U. Press, 2001)