Abstract
Given an input graph G on n vertices 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. 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 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.
This work is supported by the ANR project AGAPE (ANR-09-BLAN-0159).
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Kim, E.J., Paul, C., Philip, G. (2012). A Single-Exponential FPT Algorithm for the K 4-Minor Cover Problem. In: Fomin, F.V., Kaski, P. (eds) Algorithm Theory – SWAT 2012. SWAT 2012. Lecture Notes in Computer Science, vol 7357. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31155-0_11
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DOI: https://doi.org/10.1007/978-3-642-31155-0_11
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