• français
    • English
  • English 
    • français
    • English
  • Login
JavaScript is disabled for your browser. Some features of this site may not work without it.
BIRD Home

Browse

This CollectionBy Issue DateAuthorsTitlesSubjectsJournals BIRDResearch centres & CollectionsBy Issue DateAuthorsTitlesSubjectsJournals

My Account

Login

Statistics

View Usage Statistics

An FPT Algorithm and a Polynomial Kernel for Linear Rankwidth-1 Vertex Deletion

Thumbnail
Date
2015
Link to item file
https://hal-lirmm.ccsd.cnrs.fr/lirmm-01264011
Dewey
Principes généraux des mathématiques
Sujet
(linear) rankwidth; Distance-hereditary graphs; Thread graphs; Parameterized complexity; Kernelization
DOI
http://dx.doi.org/10.4230/LIPIcs.IPEC.2015.138
Conference name
10th International Symposium on Parameterized and Exact Computation (IPEC 2015)
Conference date
09-2015
Conference city
Patras
Conference country
Greece
Book title
IPEC: International symposium on Parameterized and Exact Computation
Publisher
Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik
ISBN
978-3-95977-140-5
URI
https://basepub.dauphine.fr/handle/123456789/21021
Collections
  • LAMSADE : Publications
Metadata
Show full item record
Author
Paul, Christophe
Kim, Eun Jung
989 Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision [LAMSADE]
Kanté, Mamadou Moustapha
Kwon, O-joung
Type
Communication / Conférence
Item number of pages
139-150
Abstract (EN)
Linear rankwidth is a linearized variant of rankwidth, introduced by Oum and Seymour [Approxi-mating clique-width and branch-width. J. Combin. Theory Ser. B, 96(4):514-528, 2006.], and it is similar to pathwidth, which is the linearized variant of treewidth. Motivated from the results on graph modification problems into graphs of bounded treewidth or pathwidth, we investigate a graph modification problem into the class of graphs having linear rankwidth at most one, called the Linear Rankwidth-1 Vertex Deletion (shortly, LRW1-Vertex Deletion). In this problem, given an n-vertex graph G and a positive integer k, we want to decide whether there is a set of at most k vertices whose removal turns G into a graph of linear rankwidth at most one and if one exists, find such a vertex set. While the meta-theorem of Courcelle, Makowsky, and Rotics implies that LRW1-Vertex Deletion can be solved in time f (k) · n 3 for some function f , it is not clear whether this problem allows a runtime with a modest exponential function. We establish that LRW1-Vertex Deletion can be solved in time 8 k · n O(1). The major obstacle to this end is how to handle a long induced cycle as an obstruction. To fix this issue, we define the necklace graphs and investigate their structural properties. We also show that the LRW1-Vertex Deletion has a polynomial kernel.

  • Accueil Bibliothèque
  • Site de l'Université Paris-Dauphine
  • Contact
SCD Paris Dauphine - Place du Maréchal de Lattre de Tassigny 75775 Paris Cedex 16

 Content on this site is licensed under a Creative Commons 2.0 France (CC BY-NC-ND 2.0) license.