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planar graph

Nov 19, 20241 min read

in graph theory, a planar graph is a graph where it is possible to make a two dimensional re-representation of the graph where there are no edges crossing

i couldn’t find a mathematical definition for this, but logically speaking, since we are limited to two dimensions, the restrictions are as follows:

any graph that contains a subgraph of $K_{5}$ , a complete graph with 5 vertices, is not planar

any graph that contains a subgraph of $K_{a, b}$ where both $a > 2$ and $b > 2$ is not planar

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planar graph

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