 Because the graphs with planar covers are closed under the operation of taking minors, it follows from the Robertson–Seymour theorem that they may be characterized by a finite set of forbidden minors.A graph is a forbidden minor for this property if it has no planar cover, but all of its minors do have planar covers.This characterization can be used to prove the existence of a polynomial time algorithm that tests for the existence of a planar cover, by searching for each of the forbidden minors and returning that a planar cover exists only if this search fails to find any of them.