License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ESA.2022.58
URN: urn:nbn:de:0030-drops-169969
Go to the corresponding LIPIcs Volume Portal

Gajarský, Jakub ; Jaffke, Lars ; Lima, Paloma T. ; Novotná, Jana ; Pilipczuk, Marcin ; Rzążewski, Paweł ; Souza, Uéverton S.

Taming Graphs with No Large Creatures and Skinny Ladders

LIPIcs-ESA-2022-58.pdf (1 MB)


We confirm a conjecture of Gartland and Lokshtanov [arXiv:2007.08761]: if for a hereditary graph class ? there exists a constant k such that no member of ? contains a k-creature as an induced subgraph or a k-skinny-ladder as an induced minor, then there exists a polynomial p such that every G ∈ ? contains at most p(|V(G)|) minimal separators. By a result of Fomin, Todinca, and Villanger [SIAM J. Comput. 2015] the latter entails the existence of polynomial-time algorithms for Maximum Weight Independent Set, Feedback Vertex Set and many other problems, when restricted to an input graph from ?. Furthermore, as shown by Gartland and Lokshtanov, our result implies a full dichotomy of hereditary graph classes defined by a finite set of forbidden induced subgraphs into tame (admitting a polynomial bound of the number of minimal separators) and feral (containing infinitely many graphs with exponential number of minimal separators).

BibTeX - Entry

  author =	{Gajarsk\'{y}, Jakub and Jaffke, Lars and Lima, Paloma T. and Novotn\'{a}, Jana and Pilipczuk, Marcin and Rz\k{a}\.{z}ewski, Pawe{\l} and Souza, U\'{e}verton S.},
  title =	{{Taming Graphs with No Large Creatures and Skinny Ladders}},
  booktitle =	{30th Annual European Symposium on Algorithms (ESA 2022)},
  pages =	{58:1--58:8},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-247-1},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{244},
  editor =	{Chechik, Shiri and Navarro, Gonzalo and Rotenberg, Eva and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{},
  URN =		{urn:nbn:de:0030-drops-169969},
  doi =		{10.4230/LIPIcs.ESA.2022.58},
  annote =	{Keywords: Minimal separator, hereditary graph class}

Keywords: Minimal separator, hereditary graph class
Collection: 30th Annual European Symposium on Algorithms (ESA 2022)
Issue Date: 2022
Date of publication: 01.09.2022

DROPS-Home | Fulltext Search | Imprint | Privacy Published by LZI