Linear Kernels on Graphs Excluding Topological Minors
Data Structures and Algorithms
2012-07-16 v4 Computational Complexity
Discrete Mathematics
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 -topological-minor free graphs, for an arbitrary fixed graph . This builds on earlier results by Fomin et al.\ on linear kernels for -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.
Cite
@article{arxiv.1201.2780,
title = {Linear Kernels on Graphs Excluding Topological Minors},
author = {Alexander Langer and Felix Reidl and Peter Rossmanith and Somnath Sikdar},
journal= {arXiv preprint arXiv:1201.2780},
year = {2012}
}
Comments
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