A Polynomial Kernel for Diamond-Free Editing
Data Structures and Algorithms
2018-05-04 v2
Abstract
An -free editing problem asks whether we can edit at most edges to make a graph contain no induced copy of the fixed graph . We obtain a polynomial kernel for this problem when is a diamond. The incompressibility dichotomy for being a 3-connected graph and the classical complexity dichotomy suggest that except for being a complete/empty graph, -free editing problems admit polynomial kernels only for a few small graphs . Therefore, we believe that our result is an essential step toward a complete dichotomy on the compressibility of -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}
}