Algorithmic implications A Kuratowski subgraph of a nonplanar graph can be found in linear time, as measured by the size of the input graph.. 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.. Usually, non-planar graphs contain a large number of Kuratowski-subgraphs. The extraction of these subgraphs is needed, e.g., in branch and cut algorithms for crossing minimization. It is possible to extract a large number of Kuratowski subgraphs in time dependent on their total size.
Algorithmic implications A Kuratowski subgraph of a nonplanar graph can be found in linear time, as measured by the size of the input graph.. 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.. Usually, non-planar graphs contain a large number of Kuratowski-subgraphs. The extraction of these subgraphs is needed, e.g., in branch and cut algorithms for crossing minimization. It is possible to extract a large number of Kuratowski subgraphs in time dependent on their total size.