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Chapter: Conditions for Planarity and Planarity Testing

Planarity testing is a very common problem in graph theory because only planar graphs have a planar embedding. In this chapter, we will learn about some necessary and sufficient criteria to decide, whether a given graph is planar or not. Also, we will learn about some methods to test a given graph for being planar. These tests can be transformed into algorithms and be programmed using a computer.

Table of Contents

Explanations: 1

1. Proposition: A Necessary Condition for a Graph to be Planar
2. Proposition: A Necessary Condition for a Graph with Shortest Cycles to Be Planar
3. Proposition: A Necessary Condition for a Graph with Shortest Cycles to Be Planar (II)
4. Proposition: Relationship Between Planarity and Connectivity of Graphs
5. Proposition: Relationship Between Planarity and Biconnectivity of Graphs

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