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arXiv · 1612.04985

Anti-Path Cover on Sparse Graph Classes

Pavel Dvořák·Dušan Knop·Tomáš Masařík
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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.

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Pavel Dvořák, Dušan Knop, Tomáš Masařík. 2016-12-15. Anti-Path Cover on Sparse Graph Classes. https://doi.org/10.4204/eptcs.233.8

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