Linear Kernels on Graphs Excluding Topological Minors

Abstract

We show that problems which 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 Fomin et al.\ on linear kernels for $H$-minor-free graphs and by Bodlaender et al.\ on graphs of bounded genus. Our framework encompasses several problems, the prominent ones being Chordal Vertex Deletion, Feedback Vertex Set and Edge Dominating Set.

19 pages. A simpler proof of the results of this paper appears in http://arxiv.org/abs/1207.0835. This new paper contains additional results

References in corpus (2)

• Rank-width and Tree-width of H-minor-free Graphs
• Structure Theorem and Isomorphism Test for Graphs with Excluded Topological Subgraphs

Cited by in corpus (2)

• Everything you always wanted to know about the parameterized complexity of Subgraph Isomorphism (but were afraid to ask)
• Planar F-Deletion: Approximation, Kernelization and Optimal FPT Algorithms