A Polynomial Kernel for Diamond-Free Editing

Authors Yixin Cao , Ashutosh Rai, R. B. Sandeep, Junjie Ye

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Yixin Cao
  • Department of Computing, Hong Kong Polytechnic University, Hong Kong, China
Ashutosh Rai
  • Department of Computing, Hong Kong Polytechnic University, Hong Kong, China
R. B. Sandeep
  • Institute for Computer Science and Control, Hungarian Academy of Sciences (MTA SZTAKI), Hungary
  • and Indian Institute of Technology Dharwad, Dharwad, India
Junjie Ye
  • Department of Computing, Hong Kong Polytechnic University, Hong Kong, China

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Yixin Cao, Ashutosh Rai, R. B. Sandeep, and Junjie Ye. A Polynomial Kernel for Diamond-Free Editing. In 26th Annual European Symposium on Algorithms (ESA 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 112, pp. 10:1-10:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)


Given a fixed graph H, the H-free editing problem asks whether we can edit at most k edges to make a graph contain no induced copy of H. We obtain a polynomial kernel for this problem when H is a diamond. The incompressibility dichotomy for H being a 3-connected graph and the classical complexity dichotomy suggest that except for H being a complete/empty graph, H-free 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.

Subject Classification

ACM Subject Classification
  • Mathematics of computing → Graph algorithms
  • Kernelization
  • Diamond-free
  • H-free editing
  • Graph modification problem


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