Linear Kernels on Graphs Excluding Topological Minors

We show that problems that have finite integer index and satisfy a requirement we call treewidth-bounding admit linear kernels on the class of H-topological-minor free graphs, for an arbitrary fixed graph H . This builds on earlier results by Bodlaender et al. on graphs of bounded genus [2] and by Fomin et al. on H-minor-free graphs [9]. Our framework encompasses several problems, the prominent ones being Chordal Vertex Deletion, Feedback Vertex Set and Edge Dominating Set.