A single-exponential FPT algorithm for the K_4-minor cover problem [article]

Eun Jung Kim and Christophe Paul and Geevarghese Philip
2012 arXiv   pre-print
Given an input graph G and an integer k, the parameterized K_4-minor cover problem asks whether there is a set S of at most k vertices whose deletion results in a K_4-minor-free graph, or equivalently in a graph of treewidth at most 2. This problem is inspired by two well-studied parameterized vertex deletion problems, Vertex Cover and Feedback Vertex Set, which can also be expressed as Treewidth-t Vertex Deletion problems: t=0 for Vertex Cover and t=1 for Feedback Vertex Set. While a
more » ... onential FPT algorithm has been known for a long time for Vertex Cover, such an algorithm for Feedback Vertex Set was devised comparatively recently. While it is known to be unlikely that Treewidth-t Vertex Deletion can be solved in time c^o(k).n^O(1), it was open whether the K_4-minor cover problem could be solved in single-exponential FPT time, i.e. in c^k.n^O(1) time. This paper answers this question in the affirmative.
arXiv:1204.1417v1 fatcat:3ygho6u2pzfihezc6tnq5cieva