License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.STACS.2019.32
URN: urn:nbn:de:0030-drops-102716
URL: https://drops.dagstuhl.de/opus/volltexte/2019/10271/
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Giannopoulou, Archontia C. ; Kwon, O-joung ; Raymond, Jean-Florent ; Thilikos, Dimitrios M.

Lean Tree-Cut Decompositions: Obstructions and Algorithms

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LIPIcs-STACS-2019-32.pdf (0.6 MB)

Abstract

The notion of tree-cut width has been introduced by Wollan in [The structure of graphs not admitting a fixed immersion, Journal of Combinatorial Theory, Series B, 110:47 - 66, 2015]. It is defined via tree-cut decompositions, which are tree-like decompositions that highlight small (edge) cuts in a graph. In that sense, tree-cut decompositions can be seen as an edge-version of tree-decompositions and have algorithmic applications on problems that remain intractable on graphs of bounded treewidth. In this paper, we prove that every graph admits an optimal tree-cut decomposition that satisfies a certain Menger-like condition similar to that of the lean tree decompositions of Thomas [A Menger-like property of tree-width: The finite case, Journal of Combinatorial Theory, Series B, 48(1):67 - 76, 1990]. This allows us to give, for every k in N, an upper-bound on the number immersion-minimal graphs of tree-cut width k. Our results imply the constructive existence of a linear FPT-algorithm for tree-cut width.

BibTeX - Entry

@InProceedings{giannopoulou_et_al:LIPIcs:2019:10271,
  author =	{Archontia C. Giannopoulou and O-joung Kwon and Jean-Florent Raymond and Dimitrios M. Thilikos},
  title =	{{Lean Tree-Cut Decompositions: Obstructions and Algorithms}},
  booktitle =	{36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019)},
  pages =	{32:1--32:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-100-9},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{126},
  editor =	{Rolf Niedermeier and Christophe Paul},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2019/10271},
  doi =		{10.4230/LIPIcs.STACS.2019.32},
  annote =	{Keywords: tree-cut width, lean decompositions, immersions, obstructions, parameterized algorithms}
}

Keywords: tree-cut width, lean decompositions, immersions, obstructions, parameterized algorithms
Collection: 36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019)
Issue Date: 2019
Date of publication: 12.03.2019

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