Partitioning H-Free Graphs of Bounded Diameter

Christoph Brause*, Petr Golovach*, Barnaby Martin*, Daniël Paulusma*, Siani Smith*

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference Contribution (Conference Proceeding)

2 Citations (Scopus)

Abstract

A natural way of increasing our understanding of NP-complete graph problems is to restrict the input to a special graph class. Classes of H-free graphs, that is, graphs that do not contain some graph H as an induced subgraph, have proven to be an ideal testbed for such a complexity study. However, if the forbidden graph H contains a cycle or claw, then these problems often stay NP-complete. A recent complexity study (MFCS 2019) on the k-Colouring problem shows that we may still obtain tractable results if we also bound the diameter of the H-free input graph. We continue this line of research by initiating a complexity study on the impact of bounding the diameter for a variety of classical vertex partitioning problems restricted to H-free graphs. We prove that bounding the diameter does not help for Independent Set, but leads to new tractable cases for problems closely related to 3-Colouring. That is, we show that Near-Bipartiteness, Independent Feedback Vertex Set, Independent Odd Cycle Transversal, Acyclic 3-Colouring and Star 3-Colouring are all polynomial-time solvable for chair-free graphs of bounded diameter. To obtain these results we exploit a new structural property of 3-colourable chair-free graphs.

Original languageEnglish
Title of host publication32nd International Symposium on Algorithms and Computation, ISAAC 2021
EditorsHee-Kap Ahn, Kunihiko Sadakane
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)9783959772143
DOIs
Publication statusPublished - 1 Dec 2021
Event32nd International Symposium on Algorithms and Computation, ISAAC 2021 - Fukuoka, Japan
Duration: 6 Dec 20218 Dec 2021

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume212
ISSN (Print)1868-8969

Conference

Conference32nd International Symposium on Algorithms and Computation, ISAAC 2021
Country/TerritoryJapan
CityFukuoka
Period6/12/218/12/21

Bibliographical note

Funding Information:
Supported by the Leverhulme Trust (RPG-2016-258).

Publisher Copyright:
© Christoph Brause, Petr Golovach, Barnaby Martin, Daniël Paulusma, and Siani Smith.

Keywords

  • Complexity dichotomy
  • Diameter
  • H-free
  • Vertex partitioning problem

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