Towards optimal kernel for connected vertex cover in planar graphs
Data Structures and Algorithms
2011-10-11 v1 Discrete Mathematics
Abstract
We study the parameterized complexity of the connected version of the vertex cover problem, where the solution set has to induce a connected subgraph. Although this problem does not admit a polynomial kernel for general graphs (unless NP is a subset of coNP/poly), for planar graphs Guo and Niedermeier [ICALP'08] showed a kernel with at most 14k vertices, subsequently improved by Wang et al. [MFCS'11] to 4k. The constant 4 here is so small that a natural question arises: could it be already an optimal value for this problem? In this paper we answer this quesion in negative: we show a (11/3)k-vertex kernel for Connected Vertex Cover in planar graphs. We believe that this result will motivate further study in search for an optimal kernel.
Cite
@article{arxiv.1110.1964,
title = {Towards optimal kernel for connected vertex cover in planar graphs},
author = {Lukasz Kowalik and Marcin Pilipczuk and Karol Suchan},
journal= {arXiv preprint arXiv:1110.1964},
year = {2011}
}