Planar graph
Definition
A graph 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 , and each edge is a simple arc from to . 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 in the plane. The complete graph is planar. and are not planar. Kuratowski's theorem characterizes the finite planar graphs by these two graphs.
Where this leads
11 pages build on this one.
Further reading
- Web https://en.wikipedia.org/wiki/Planar_graph, lead section
About this page
| Tag | 029JQEK15B |
|---|---|
| URI | m2://029JQEK15B |
| Kind | definition |
| Writing | W1 stated |
| MSC | 05C10 |
| Defines | Planar graph |
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What this page needs for W2
- edge instance_of in: one example (0 of 1)
- edge not_instance_of in: one non-example that fails one clause (0 of 1)
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What links here
Used by
- K5 and K3,3 are not planar
- Five colour theorem
- Kuratowski's theorem
- Four colour theorem
- Euler's formula for planar graphs
- Wagner's theorem
- Dual graph
- Grötzsch's theorem