SWAT 2012: Algorithm Theory – SWAT 2012 pp 119-130

# A Single-Exponential FPT Algorithm for the K4-Minor Cover Problem

• Eun Jung Kim
• Christophe Paul
• Geevarghese Philip
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7357)

## Abstract

Given an input graph G on n vertices and an integer k, the parameterized K4-minor cover problem asks whether there is a set S of at most k vertices whose deletion results in a K4-minor free graph or, equivalently, in a graph of treewidth at most 2. The problem can thus also be called Treewidth-2 Vertex Deletion. This problem is inspired by two well-studied parameterized vertex deletion problems, Vertex Cover and Feedback Vertex Set, which can be expressed as Treewidth-t Vertex Deletion problems: t = 0 for Vertex Cover and t = 1 for Feedback Vertex Set. While a single-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 co(k)·nO(1), it was open whether the K4-minor cover could be solved in single-exponential FPT time, i.e. in ck·nO(1) time. This paper answers this question in the affirmative.

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## Authors and Affiliations

• Eun Jung Kim
• 1
• Christophe Paul
• 2
• Geevarghese Philip
• 3