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A Polynomial Kernel for Diamond-Free Editing

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

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Author Details

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

Funding

Supported in part by NSFC under grant 61572414, RGC under grants 152261 and 252026, and ERC under grant 725978.

Cite AsGet BibTex

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)
https://doi.org/10.4230/LIPIcs.ESA.2018.10

Abstract

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
Keywords
  • Kernelization
  • Diamond-free
  • H-free editing
  • Graph modification problem

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References

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