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Partitioning H-free graphs of bounded diameter

Brause, C. and Golovach, P.A. and Martin, B. and Paulusma, D. and Smith, S. (2021) 'Partitioning H-free graphs of bounded diameter.', ISAAC 2021 Fukuoka / Online, 6-8 Dec 2021.

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.

Item Type:Conference item (Paper)
Full text:Publisher-imposed embargo
(AM) Accepted Manuscript
Available under License - Creative Commons Attribution 3.0.
File format - PDF
(578Kb)
Status:Peer-reviewed
Publisher Web site:https://drops.dagstuhl.de/opus/institut_lipics.php
Date accepted:06 September 2021
Date deposited:25 October 2021
Date of first online publication:2021
Date first made open access:No date available

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