No complete graph with more than four vertices falls into this class and dual graphs only exist for those graphs that do fall into this grouping.
The most common algorithm to test for this property was developed by Auslander and Parter. By Kuratowski's Theorem, a graph only fits into this class if it is neither a K5 nor a K3,3 subdivision. No complete graph with more than four vertices falls into this class and dual graphs only exist for those graphs that do fall into this grouping. Euler's formula can be used to relate the number of vertices, edges, and faces, while perhaps the most famous theorem dealing with them states that they can always be properly colored with four colors. For ten points, name this graph type characterized by having an embedding in the plane where no two edges cross.
The most common algorithm to test for this property was developed by Auslander and Parter.
{Planar} Graph