MSOL restricted contractibility to planar graphs

As a specific example, we can solve the ℓ-subgraph contractibility problem in which the edges of the set S are required to form disjoint connected subgraphs of size at most ℓ. This problem can be solved in time O(n2f′(k,ℓ)) using the general algorithm. We also show that for ℓ≥2 the problem is NP-complete.