English

Polynomial kernels for 3-leaf power graph modification problems

Discrete Mathematics 2015-05-13 v2 Data Structures and Algorithms

Abstract

A graph G=(V,E) is a 3-leaf power iff there exists a tree T whose leaves are V and such that (u,v) is an edge iff u and v are at distance at most 3 in T. The 3-leaf power graph edge modification problems, i.e. edition (also known as the closest 3-leaf power), completion and edge-deletion, are FTP when parameterized by the size of the edge set modification. However polynomial kernel was known for none of these three problems. For each of them, we provide cubic kernels that can be computed in linear time for each of these problems. We thereby answer an open problem first mentioned by Dom, Guo, Huffner and Niedermeier (2005).

Keywords

Cite

@article{arxiv.0809.2858,
  title  = {Polynomial kernels for 3-leaf power graph modification problems},
  author = {Stephane Bessy and Christophe Paul and Anthony Perez},
  journal= {arXiv preprint arXiv:0809.2858},
  year   = {2015}
}

Comments

Submitted

R2 v1 2026-06-21T11:20:59.351Z