Detecting induced star-like minors in polynomial time

The INDUCED MINOR problem is to test whether a graph G contains a graph H as an induced minor, i.e., if G can be modified into H by a sequence of vertex deletions and edge contractions. When H is fixed, i.e., not part of the input, this problem is denoted H -INDUCED MINOR. We provide polynomialtime algorithms for this problem in the case that the fixed target graph has a starlike structure. In particular, we show polynomial-time solvability for all forests H on at most seven vertices except for one such case.