Planar Graphs 

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1.Definition: Planar Drawing (Embedding) 

2.Definition: Planar Graph 

3.Proposition: Relationship Between Planarity and Biconnectivity of Graphs 

4.Definition: Pieces of a Graph With Respect to A Cycle 

5.Definition: Separating and Non-Separating Cycles 

6.Definition: Interlacing Pieces with Respect to a Cycle, Interlacement Graph 

7.Definition: Subdivision of a Graph 

8.Proposition: Relationship Between Planarity and Connectivity of Graphs 

9.Lemma: When is it possible to find a separating cycle in a biconnected graph, given a non-separating cycle? 

10.Theorem: Characterization of Biconnected Planar Graphs 

11.Theorem: Characterization of Planar Graphs (Kuratowski)