A Polynomial Kernel for Diamond-Free Editing
نویسندگان
چکیده
An H-free editing problem asks whether we can edit at most k edges to make a graph contain no induced copy of the fixed graph H. We obtain a polynomial kernel for this problem when H is a diamond. The incompressibility dichotomy for H being a 3-connected graph [4] and the classical complexity dichotomy [1] suggest that except for H being a complete/empty graph, Hfree editing problems admit polynomial kernels only for a few small graphs H. Therefore, we believe that our result is an essential step toward a complete dichotomy on the compressibility of H-free editing. Additionally, we give a cubic-vertex kernel for the diamond-free edge deletion problem, which is far simpler than the previous kernel of the same size for the problem. 2012 ACM Subject Classification G.2.2 Graph Algorithms, I.1.2 Analysis of Algorithms
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