PlanarGraphQ

PlanarGraphQ[g] yields True if graph g can be drawn in a plane without edge crossings, and False otherwise.

Examples

Test for planarity:

PlanarGraphQ[CompleteGraph[4]]
(* True - K4 is planar *)

PlanarGraphQ[CompleteGraph[5]]
(* False - K5 is not planar *)

Grid graphs are planar:

PlanarGraphQ[GridGraph[{10, 10}]]
(* True *)

Please visit the official Wolfram Language Reference for more details.