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Queue Layouts of Planar 3-Trees

  • Jawaherul Md. Alam
  • Michael A. Bekos
  • Martin GronemannEmail author
  • Michael Kaufmann
  • Sergey Pupyrev
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11282)

Abstract

A queue layout of a graph G consists of a linear order of the vertices of G and a partition of the edges of G into queues, so that no two independent edges of the same queue are nested. The queue number of G is the minimum number of queues required by any queue layout of G. In this paper, we continue the study of the queue number of planar 3-trees. As opposed to general planar graphs, whose queue number is not known to be bounded by a constant, the queue number of planar 3-trees has been shown to be at most seven. In this work, we improve the upper bound to five. We also show that there exist planar 3-trees, whose queue number is at least four; this is the first example of a planar graph with queue number greater than three.

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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Jawaherul Md. Alam
    • 1
  • Michael A. Bekos
    • 2
  • Martin Gronemann
    • 3
    Email author
  • Michael Kaufmann
    • 2
  • Sergey Pupyrev
    • 1
  1. 1.Department of Computer ScienceUniversity of ArizonaTucsonUSA
  2. 2.Institut für InformatikUniversität TübingenTübingenGermany
  3. 3.Institut für InformatikUniversität zu KölnKölnGermany

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