A singleexponential FPT algorithm for the $K_4$minor cover problem
Abstract
Given an input graph G and an integer k, the parameterized K_4minor cover problem asks whether there is a set S of at most k vertices whose deletion results in a K_4minorfree graph, or equivalently in a graph of treewidth at most 2. This problem is inspired by two wellstudied parameterized vertex deletion problems, Vertex Cover and Feedback Vertex Set, which can also be expressed as Treewidtht Vertex Deletion problems: t=0 for Vertex Cover and t=1 for Feedback Vertex Set. While a singleexponential FPT algorithm has been known for a long time for \textsc{Vertex Cover}, such an algorithm for Feedback Vertex Set was devised comparatively recently. While it is known to be unlikely that Treewidtht Vertex Deletion can be solved in time c^{o(k)}.n^{O(1)}, it was open whether the K_4minor cover problem could be solved in singleexponential FPT time, i.e. in c^k.n^{O(1)} time. This paper answers this question in the affirmative.
 Publication:

arXiv eprints
 Pub Date:
 April 2012
 arXiv:
 arXiv:1204.1417
 Bibcode:
 2012arXiv1204.1417K
 Keywords:

 Computer Science  Data Structures and Algorithms;
 Computer Science  Computational Complexity;
 Computer Science  Discrete Mathematics