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Cox, Mary A.

Mathematics

2005

MS

A graph is planar if it can be drawn in the plane without edge crossings. Kuratowski's Theorem says that the minimal non-planar graphs are either the complete graph on five vertices or the complete bipartite graph with three vertices in each part. These graphs are non-planar, but removing any edge makes a planar graph. In this thesis, we study the minimal non-planar graphs under the induced subgraph order; that is, the graphs are non-planar, but removing any vertex makes a planar graph.