Graph Theory: 62. Graph Minors and Wagner's Theorem 

In this video, we begin with a visualisation of an edge contraction and discuss the fact that an edge contraction may be thought of as resulting in a multigraph or simple graph, depending on the application. We then state the definition a contraction of edge e in a graph G resulting in a simple graph G/e. Next we define graph minors and state Wagner's Theorem, which gives a characterisation of planar graphs. Finally, we compare Wagner's Theorem with Kuratowski's Theorem.
-- Bits of Graph Theory by Dr. Sarada Herke.
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