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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.

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    http://en.wikipedia.org/wiki/Planar_graph#Kuratowski.27s_and_Wagner.27s_theorems2010-11-12
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    The fundamental group is not very useful in this context, as each finite graph is homotopy equivalent to a bouquet of circles.2010-11-12

3 Answers 3