• xmlui.mirage2.page-structure.header.title
    • français
    • English
  • Help
  • Login
  • Language 
    • Français
    • English
View Item 
  •   BIRD Home
  • LAMSADE (UMR CNRS 7243)
  • LAMSADE : Publications
  • View Item
  •   BIRD Home
  • LAMSADE (UMR CNRS 7243)
  • LAMSADE : Publications
  • View Item
JavaScript is disabled for your browser. Some features of this site may not work without it.

Browse

BIRDResearch centres & CollectionsBy Issue DateAuthorsTitlesTypeThis CollectionBy Issue DateAuthorsTitlesType

My Account

LoginRegister

Statistics

Most Popular ItemsStatistics by CountryMost Popular Authors
Thumbnail

Maximum Independent Sets in Subcubic Graphs: New Results

Harutyunyan, Ararat; Lampis, Michael; Lozin, Vadim; Monnot, Jérôme (2019), Maximum Independent Sets in Subcubic Graphs: New Results, in Sau, Ignasi; Thilikos, Dimitrios M., Graph-Theoretic Concepts in Computer Science, Revised Papers, Springer International Publishing : Berlin Heidelberg, p. 40-52. 10.1007/978-3-030-30786-8_4

View/Open
1810.10940.pdf (220.4Kb)
Type
Communication / Conférence
Date
2019
Conference title
45th International Workshop on Graph-Theoretic Concepts in Computer Science (WG 2019)
Conference date
2019-06
Conference city
Vall de Núria
Conference country
Spain
Book title
Graph-Theoretic Concepts in Computer Science, Revised Papers
Book author
Sau, Ignasi; Thilikos, Dimitrios M.
Publisher
Springer International Publishing
Published in
Berlin Heidelberg
ISBN
978-3-030-30785-1
Number of pages
394
Pages
40-52
Publication identifier
10.1007/978-3-030-30786-8_4
Metadata
Show full item record
Author(s)
Harutyunyan, Ararat
Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision [LAMSADE]
Lampis, Michael cc
Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision [LAMSADE]
Lozin, Vadim
Warwick Mathematics Institute [WMI]
Monnot, Jérôme cc
Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision [LAMSADE]
Abstract (EN)
We consider the complexity of the classical Independent Set problem on classes of subcubic graphs characterized by a finite set of forbidden induced subgraphs. It is well-known that a necessary condition for Independent Set to be tractable in such a class (unless P = NP) is that the set of forbidden induced subgraphs includes a subdivided star Sk,k,k, for some k. Here, Sk,k,kis the graph obtained by taking three paths of length k and identifying one of their endpoints.It is an interesting open question whether this condition is also sufficient: is Independent Set tractable on all hereditary classes of subcubic graphs that exclude some Sk,k,k? A positive answer to this question would provide a complete classification of the complexity of Independent Set on all classes of subcubic graphs characterized by a finite set of forbidden induced subgraphs. The best currently known result of this type is tractability for S2,2,2-free graphs. In this paper we generalize this result by showing that the problem remains tractable on S2,k,k-free graphs, for any fixed k. Along the way, we show that subcubic Independent Set is tractable for graphs excluding a type of graph we call an “apple with a long stem”, generalizing known results for apple-free graphs.
Subjects / Keywords
Independent set; Sub-Cubic graphs; Apple-Free graphs

Related items

Showing items related by title and author.

  • Thumbnail
    Maximum Independent Sets in Subcubic Graphs: New Results 
    Harutyunyan, Ararat; Lampis, Michael; Lozin, Vadim; Monnot, Jérôme (2019) Communication / Conférence
  • Thumbnail
    Maximum independent sets in subcubic graphs: New results 
    Harutyunyan, Ararat; Lampis, Michael; Lozin, V.; Monnot, Jérôme (2020) Article accepté pour publication ou publié
  • Thumbnail
    On the maximum independent set problem in subclasses of subcubic graphs 
    Ries, Bernard; Monnot, Jérôme; Lozin, Vadim (2015) Article accepté pour publication ou publié
  • Thumbnail
    On the Maximum Independent Set Problem in Subclasses of Subcubic Graphs 
    Lozin, Vadim; Monnot, Jérôme; Ries, Bernard (2013) Communication / Conférence
  • Thumbnail
    Extension of Vertex Cover and Independent Set in Some Classes of Graphs 
    Casel, Katrin; Fernau, Henning; Khosravian Ghadikolaei, Mehdi; Monnot, Jérôme; Sikora, Florian (2019) Communication / Conférence
Dauphine PSL Bibliothèque logo
Place du Maréchal de Lattre de Tassigny 75775 Paris Cedex 16
Phone: 01 44 05 40 94
Contact
Dauphine PSL logoEQUIS logoCreative Commons logo