Anti-Path Cover on Sparse Graph Classes
Data Structures and Algorithms
2016-12-16 v1 Discrete Mathematics
Abstract
We show that it is possible to use Bondy-Chvatal closure to design an FPT algorithm that decides whether or not it is possible to cover vertices of an input graph by at most k vertex disjoint paths in the complement of the input graph. More precisely, we show that if a graph has tree-width at most w and its complement is closed under Bondy-Chvatal closure, then it is possible to bound neighborhood diversity of the complement by a function of w only. A simpler proof where tree-depth is used instead of tree-width is also presented.
Cite
@article{arxiv.1612.04985,
title = {Anti-Path Cover on Sparse Graph Classes},
author = {Pavel Dvořák and Dušan Knop and Tomáš Masařík},
journal= {arXiv preprint arXiv:1612.04985},
year = {2016}
}
Comments
In Proceedings MEMICS 2016, arXiv:1612.04037