2 research outputs found
Towards optimal kernel for connected vertex cover in planar graphs
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