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Transforming Stacks into Queues: Mixed and Separated Layouts of Graphs

Authors Julia Katheder , Michael Kaufmann , Sergey Pupyrev , Torsten Ueckerdt

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Author Details

Julia Katheder
  • Wilhelm-Schickard-Institut für Informatik, Universität Tübingen, Germany
Michael Kaufmann
  • Wilhelm-Schickard-Institut für Informatik, Universität Tübingen, Germany
Sergey Pupyrev
  • Menlo Park, CA, USA
Torsten Ueckerdt
  • Institute of Theoretical Informatics, Karlsruhe Institute of Technology, Germany

Funding

  • Katheder, Julia: The work of J. Katheder is supported by DFG grant Ka 812-18/2.
  • Kaufmann, Michael: The work of M. Kaufmann is supported by DFG grant Ka 812-18/2.
  • Ueckerdt, Torsten: The work of T. Ueckerdt is supported by DFG - 520723789.

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Julia Katheder, Michael Kaufmann, Sergey Pupyrev, and Torsten Ueckerdt. Transforming Stacks into Queues: Mixed and Separated Layouts of Graphs. In 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 327, pp. 56:1-56:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.STACS.2025.56

Abstract

Some of the most important open problems for linear layouts of graphs ask for the relation between a graph’s queue number and its stack number or mixed number. In such, we seek a vertex order and edge partition of G into parts with pairwise non-crossing edges (a stack) or with pairwise non-nesting edges (a queue). Allowing only stacks, only queues, or both, the minimum number of required parts is the graph’s stack number sn(G), queue number qn(G), and mixed number mn(G), respectively.
Already in 1992, Heath and Rosenberg asked whether qn(G) is bounded in terms of sn(G), that is, whether stacks "can be transformed into" queues. This is equivalent to bipartite 3-stack graphs having bounded queue number (Dujmović and Wood, 2005). Recently, Alam et al. asked whether qn(G) is bounded in terms of mn(G), which we show to also be equivalent to the previous questions.
We approach the problem by considering separated linear layouts of bipartite graphs. In this natural setting all vertices of one part must precede all vertices of the other part. Separated stack and queue numbers coincide, and for fixed vertex orders, graphs with bounded separated stack/queue number can be characterized and efficiently recognized, whereas the separated mixed layouts are more challenging. In this work, we thoroughly investigate the relationship between separated and non-separated, mixed and pure linear layouts.

Subject Classification

ACM Subject Classification
  • Mathematics of computing → Graph theory
  • Mathematics of computing → Combinatorics
Keywords
  • Separated linear Layouts
  • Stack Number
  • Queue Number
  • mixed Number
  • bipartite Graphs

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References

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