A Polynomial Kernel for Diamond-Free Editing

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

Research output: Journal article publicationJournal articleAcademic researchpeer-review


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.

Original languageEnglish
Pages (from-to)197-215
Number of pages19
Issue number1
Publication statusPublished - Jan 2022


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

ASJC Scopus subject areas

  • Computer Science(all)
  • Computer Science Applications
  • Applied Mathematics


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