Schloss Dagstuhl - Leibniz-Zentrum für Informatik GmbH Schloss Dagstuhl - Leibniz-Zentrum für Informatik GmbH scholarly article en Brause, Christoph; Golovach, Petr; Martin, Barnaby; Paulusma, Daniël; Smith, Siani https://www.dagstuhl.de/lipics License: Creative Commons Attribution 4.0 license (CC BY 4.0)
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URN: urn:nbn:de:0030-drops-154543
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Partitioning H-Free Graphs of Bounded Diameter

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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.

BibTeX - Entry

@InProceedings{brause_et_al:LIPIcs.ISAAC.2021.21,
  author =	{Brause, Christoph and Golovach, Petr and Martin, Barnaby and Paulusma, Dani\"{e}l and Smith, Siani},
  title =	{{Partitioning H-Free Graphs of Bounded Diameter}},
  booktitle =	{32nd International Symposium on Algorithms and Computation (ISAAC 2021)},
  pages =	{21:1--21:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-214-3},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{212},
  editor =	{Ahn, Hee-Kap and Sadakane, Kunihiko},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2021/15454},
  URN =		{urn:nbn:de:0030-drops-154543},
  doi =		{10.4230/LIPIcs.ISAAC.2021.21},
  annote =	{Keywords: vertex partitioning problem, H-free, diameter, complexity dichotomy}
}

Keywords: vertex partitioning problem, H-free, diameter, complexity dichotomy
Seminar: 32nd International Symposium on Algorithms and Computation (ISAAC 2021)
Issue date: 2021
Date of publication: 30.11.2021


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