An improved linear kernel for the cycle contraction problem

The problem of modifying a given graph to satisfy certain properties has been one of the central topics in parameterized tractability study. In this paper, we investigate the cycle contraction problem, which makes a graph into a cycle by edge contractions. The problem was raised by Belmonte et al. [IPEC 2013] and they obtained a linear kernel with at most 6k+6 vertices for it. We provide an improved kernel with at most 5k+4 vertices for the problem in this paper. Our result showcases how to design kernelization algorithm for one problem by exploiting kernels of another problem.