Kernels for F-Deletion

How close is a graph to being acyclic, or planar, or of small treewidth? Many such properties are captured by forbidden minors, which leads to F-Deletion: delete at most k vertices so that no graph from a fixed family F remains as a minor. A conjecture says that F-Deletion has polynomial kernels exactly when F contains a planar graph. In my thesis defence I gather evidence for it: an approximation algorithm, polynomial kernels on claw-free graphs and whenever F contains θ_c (two vertices joined by c parallel edges), an Erdős–Pósa property for θ_c, and the protrusion-based reductions behind them. I also cover Independent Feedback Vertex Set and Colorful Motifs.