Planarity

However, there exist fast algorithms for this problem: for a graph with n vertices, it is possible to determine in time (n) (linear time) whether the graph may be planar or not (see planarity testing ).

Note that these theorems provide necessary conditions for planarity that are not sufficient conditions, and therefore can only be used to prove a graph is not planar, not that it is planar.

Other planarity criteria In practice, it is difficult to use Kuratowski's criterion to quickly decide whether a given graph is planar.

This allows the correctness of a planarity testing algorithm to be verified for nonplanar inputs, as it is straightforward to test whether a given subgraph is or is not a Kuratowski subgraph. citation.