Marcin Kaminski
Deciding more containment relations in planar graphs in FPT time

We consider several containment relations - contractions, (surface)
topological minors, weak and strong immersions - and show how to decide
those relations for planar host graphs in FPT time when parameterized by
the size of the pattern graph. We also discuss how to extend the results
beyond planarity - to classes of inputs with an excluded minor.