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Recognizing k-equistable Graphs in FPT Time

  • Eun Jung Kim
  • Martin Milanič
  • Oliver SchaudtEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9224)

Abstract

A graph \(G = (V,E)\) is called equistable if there exist a positive integer t and a weight function \(w : V \rightarrow \mathbb {N}\) such that \(S \subseteq V\) is a maximal stable set of G if and only if \(w(S) = t\). Such a function w is called an equistable function of G. For a positive integer k, a graph \(G = (V,E)\) is said to be k-equistable if it admits an equistable function which is bounded by k.

We prove that the problem of recognizing k-equistable graphs is fixed parameter tractable when parameterized by k, affirmatively answering a question of Levit et al. In fact, the problem admits an \(O(k^5)\)-vertex kernel that can be computed in linear time.

Keywords

Equistable graphs Recognition algorithm Fixed parameter tractability 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Eun Jung Kim
    • 1
  • Martin Milanič
    • 2
  • Oliver Schaudt
    • 3
    Email author
  1. 1.CNRS-Université Paris-DauphineParis Cedex 16France
  2. 2.UP IAM and UP FAMNITUniversity of PrimorskaKoperSlovenia
  3. 3.Universität zu KölnInstitut Für InformatikKölnGermany

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