Editing P (complexity) (section)

==Pure existence proofs of polynomial-time algorithms==
Some problems are known to be solvable in polynomial time, but no concrete algorithm is known for solving them. For example, the [[Robertson–Seymour theorem]] guarantees that there is a finite list of [[forbidden minor]]s that characterizes (for example) the set of graphs that can be embedded on a torus; moreover, Robertson and Seymour showed that there is an O(''n''<sup>3</sup>) algorithm for determining whether a graph has a given graph as a minor. This yields a [[nonconstructive proof]] that there is a polynomial-time algorithm for determining if a given graph can be embedded on a torus, despite the fact that no concrete algorithm is known for this problem.