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Planar graph

Graph theory and combinatorics

A graph that can be drawn in the plane with no two edges crossing.

What is usually left out

Planarity is a property of the graph, not of a particular drawing — a graph is planar if some crossing-free drawing exists, however badly it is usually drawn. Kuratowski characterised planarity exactly: a graph is planar precisely when it contains no subdivision of the complete graph on five vertices or of the complete bipartite graph on three plus three.

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