  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.
