The planar graph test
Planar graphs are graphs that can be drawn on a plane without any intersecting edges. In order to draw them, you have to start from a vertex, draw from edge to edge, and keep track of the faces as the drawing continues. According to Kuratowski, a graph is planar if it does not contain a subgraph that is part of the complete graph on five vertices.
The following is a simple example of a planar graph:
Euler's formula connects a number of vertices, edges, and faces. According to Euler's formula, if a finite and connected planar graph is drawn in the plane without any intersecting edge, and if v represents the number of vertices, ...
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