Graph minors. XIII: the disjoint paths problem
Journal of Combinatorial Theory Series B
A Linear-Time Algorithm for Finding Tree-Decompositions of Small Treewidth
SIAM Journal on Computing
Journal of the ACM (JACM)
Computing crossing numbers in quadratic time
Journal of Computer and System Sciences - STOC 2001
Obtaining a Planar Graph by Vertex Deletion
Algorithmica
On graph contractions and induced minors
Discrete Applied Mathematics
| Hi-index | 0.00 |
We study the computational complexity of graph planarization via edge contraction. The problem Contract asks whether there exists a set S of at most k edges that when contracted produces a planar graph. We give an FPT algorithm in time $\mathcal{O}(n^2 f(k))$ which solves a more general problem P-RestrictedContract in which S has to satisfy in addition a fixed inclusion-closed MSOL formula P. For different formulas P we get different problems. As a specific example, we study the ℓ-subgraph contractability problem in which edges of a set S are required to form disjoint connected subgraphs of size at most ℓ. This problem can be solved in time $\mathcal{O}(n^2 f'(k,l))$ using the general algorithm. We also show that for ℓ≥2 the problem is NP-complete. And it remains NP-complete when generalized for a fixed genus (instead of planar graphs).