Math 2.0

Combinatorics Definition

Planar graph

Definition

A graph GG is planar if it has a drawing in the plane in which no two edges cross. In such a drawing, the vertices are distinct points of ℝ2\mathbb{R}^2, and each edge uvuv is a simple arc from uu to vv. Two arcs meet only at a common end, and an arc contains no vertex other than its ends.

Remarks

A drawing of this kind is a plane graph, or an embedding of GG in the plane. The complete graph K4K_4 is planar. K5K_5 and K3,3K_{3,3} are not planar. Kuratowski's theorem characterizes the finite planar graphs by these two graphs.

Where this leads

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Further reading

  1. Web https://en.wikipedia.org/wiki/Planar_graph, lead section
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