Improved kernel results for some FPT problems based on simple observations

In this paper, we study the kernelization algorithms for several parameterized problems, including Parameterized Co-Path Set problem, Parameterized Path-Contractibility problem and Parameterized Connected Dominating Set on G7 Graphs problem. Based on simple observations, we give simple kernelization algorithms with kernel sizes 4k, 3k+4, and O(k2), respectively, which improves the previous best results 6k, 5k+3, and O(k3), respectively.