English

A Polynomial Kernel for Diamond-Free Editing

Data Structures and Algorithms 2018-05-04 v2

Abstract

An HH-free editing problem asks whether we can edit at most kk edges to make a graph contain no induced copy of the fixed graph HH. We obtain a polynomial kernel for this problem when HH is a diamond. The incompressibility dichotomy for HH being a 3-connected graph and the classical complexity dichotomy suggest that except for HH being a complete/empty graph, HH-free editing problems admit polynomial kernels only for a few small graphs HH. Therefore, we believe that our result is an essential step toward a complete dichotomy on the compressibility of HH-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.

Cite

@article{arxiv.1803.03358,
  title  = {A Polynomial Kernel for Diamond-Free Editing},
  author = {Yixin Cao and Ashutosh Rai and R. B. Sandeep and Junjie Ye},
  journal= {arXiv preprint arXiv:1803.03358},
  year   = {2018}
}
R2 v1 2026-06-23T00:47:17.276Z