A Single-Exponential FPT Algorithm for the K 4-Minor Cover Problem [chapter]

Eun Jung Kim, Christophe Paul, Geevarghese Philip
2012 Lecture Notes in Computer Science  
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 » ... le-exponential 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 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.
doi:10.1007/978-3-642-31155-0_11 fatcat:gqnrcyxuvnbzdk32fujb3bguna