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Structural Parameterizations for Boxicity

  • Henning BruhnEmail author
  • Morgan Chopin
  • Felix Joos
  • Oliver Schaudt
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8747)

Abstract

The boxicity of a graph \(G\) is the least integer \(d\) such that \(G\) has an intersection model of axis-aligned \(d\)-dimensional boxes. Boxicity, the problem of deciding whether a given graph \(G\) has boxicity at most \(d\), is NP-complete for every fixed \(d \ge 2\). We show that Boxicity is fixed-parameter tractable when parameterized by the cluster vertex deletion number of the input graph. This generalizes the result of Adiga et al. [4], that Boxicity is fixed-parameter tractable in the vertex cover number. Moreover, we show that Boxicity admits an additive \(1\)-approximation when parameterized by the pathwidth of the input graph.

Finally, we provide evidence in favor of a conjecture of Adiga et al. [4] that Boxicity remains NP-complete even on graphs of constant treewidth.

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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Henning Bruhn
    • 1
    Email author
  • Morgan Chopin
    • 1
  • Felix Joos
    • 1
  • Oliver Schaudt
    • 2
  1. 1.Institut Für Optimierung Und Operations ResearchUniversität UlmUlmGermany
  2. 2.Institut Für InformatikUniversität Zu KölnKölnGermany

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