Part: Planar Graphs
Graphs, that can be drawn in the plane without edges being crossed are called planar graphs. Planar graphs occur in many practical problems, for instance in the design of printed circuit boards, on which conducting strings may not cross, since it would lead to undesirable electrical contact at crossing points.
In this part, we will study the properties of planar graphs and investigate, under which circumstances a given graph is planar or not planar. Moreover, we will explain the term dual graph and describe its properties.
Table of Contents
 Definition: Planar Drawing (Embedding)
 Definition: Planar Graph
 Definition: Face, Infinite Face
 Definition: Face Degree
 Lemma: Handshaking Lemma for Planar Graphs
 Theorem: Euler Characteristic for Planar Graphs
 Definition: Dual Planar Graph
 Chapter: Conditions for Planarity and Planarity Testing
 Definition: Pieces of a Graph With Respect to A Cycle
 Definition: Separating and NonSeparating Cycles
 Definition: Interlacing Pieces with Respect to a Cycle, Interlacement Graph
 Definition: Subdivision of a Graph
 Lemma: When is it possible to find a separating cycle in a biconnected graph, given a nonseparating cycle?
 Theorem: Characterization of Biconnected Planar Graphs
 Theorem: Characterization of Planar Graphs
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