Noun
planarity (countable and uncountable, plural planarities)
The condition of being 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. Source: Internet
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 ). Source: Internet
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. Source: Internet
Other planarity criteria In practice, it is difficult to use Kuratowski's criterion to quickly decide whether a given graph is planar. Source: Internet