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Recognizing Weighted Disk Contact Graphs

  • Boris Klemz
  • Martin Nöllenburg
  • Roman Prutkin
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9411)

Abstract

Disk contact representations realize graphs by mapping vertices bijectively to interior-disjoint disks in the plane such that two disks touch each other if and only if the corresponding vertices are adjacent in the graph. Deciding whether a vertex-weighted planar graph can be realized such that the disks’ radii coincide with the vertex weights is known to be \(\textsf {NP}\)-hard. In this work, we reduce the gap between hardness and tractability by analyzing the problem for special graph classes. We show that it remains \(\textsf {NP}\)-hard for outerplanar graphs with unit weights and for stars with arbitrary weights, strengthening the previous hardness results. On the positive side, we present constructive linear-time recognition algorithms for caterpillars with unit weights and for embedded stars with arbitrary weights.

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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Boris Klemz
    • 1
  • Martin Nöllenburg
    • 2
  • Roman Prutkin
    • 3
  1. 1.Institute of Computer ScienceFreie Universität BerlinBerlinGermany
  2. 2.Algorithms and Complexity Group, TU WienViennaAustria
  3. 3.Institute of Theoretical InformaticsKarlsruhe Institute of TechnologyKarlsruheGermany

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