A 9k kernel for nonseparating independent set in planar graphs

Abstract

We study kernelization (a kind of efficient preprocessing) for NP-hard problems on planar graphs. Our main result is a kernel of size at most 9k vertices for the Planar Maximum Nonseparating Independent Set problem. A direct consequence of this result is that Planar Connected Vertex Cover has no kernel with at most 9/8k vertices, assuming P∈≠∈NP. We also show a very simple 5k-vertices kernel for Planar Max Leaf, which results in a lower bound of 5/4k vertices for the kernel of Planar Connected Dominating Set (also under P∈≠∈NP). © 2012 Springer-Verlag Berlin Heidelberg.