A linear kernel for planar feedback vertex set

Abstract

In this paper we show that Feedback Vertex Set on planar graphs has a kernel of size at most 112k*. We give a polynomial time algorithm, that given a planar graph G finds a equivalent planar graph G' with at most 112k*vertices, where k* is the size of the minimum Feedback Vertex Set of G. The kernelization algorithm is based on a number of reduction rules. The correctness of most of these rules is shown using a new notion: bases of induced subgraphs. We also show how to use this new notion to automatically prove safeness of reduction rules and obtain tighter bounds for the size of the kernel. © 2008 Springer-Verlag Berlin Heidelberg.