A kernel of order 2k−c2k−c for Vertex Cover

The best known kernel for the vertex cover problem was of order 2k2k for a long time, by a result of Chen et al. Recently, results by Chlebík and Clebíková, have implied that this can be improved to 2k−12k−1. In this paper, we provide a new structural result which can be used to improve this to 2k−c2k−c, for any constant cc.