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Planar graphs of bounded degree have bounded queue number

Published: 23 June 2019 Publication History

Abstract

A queue layout of a graph consists of a linear order of its vertices and a partition of its edges into queues, so that no two independent edges of the same queue are nested. The queue number of a graph is the minimum number of queues required by any of its queue layouts. A long-standing conjecture by Heath, Leighton and Rosenberg states that the queue number of planar graphs is bounded.This conjecture has been partially settled in the positive for several sub- families of planar graphs (most of which have bounded treewidth).
In this paper, we make a further important step towards settling this conjecture. We prove that planar graphs of bounded degree (which may have unbounded treewidth) have bounded queue number. A notable implication of this result is that every planar graph of bounded degree admits a three-dimensional straight-line grid drawing in linear volume. Further implications are that every planar graph of bounded degree has bounded track number, and that every k-planar graph (i.e., every graph that can be drawn in the plane with at most k crossings per edge) of bounded degree as bounded queue number.

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1137/130908051 Planar Graphs of Bounded Degree have Bounded Queue Number STOC ’19, June 23–26, 2019, Phoenix, AZ, USA
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Cited By

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  • (2022)Code generation criteria for buffered exposed datapath architectures from dataflow graphsProceedings of the 23rd ACM SIGPLAN/SIGBED International Conference on Languages, Compilers, and Tools for Embedded Systems10.1145/3519941.3535076(133-145)Online publication date: 14-Jun-2022
  • (2019)Planar Graphs have Bounded Queue-Number2019 IEEE 60th Annual Symposium on Foundations of Computer Science (FOCS)10.1109/FOCS.2019.00056(862-875)Online publication date: Nov-2019

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cover image ACM Conferences
STOC 2019: Proceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing
June 2019
1258 pages
ISBN:9781450367059
DOI:10.1145/3313276
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Publication History

Published: 23 June 2019

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Author Tags

  1. Queue number
  2. graph algorithms
  3. planar graphs

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  • DAAD
  • MIUR

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View all
  • (2022)Code generation criteria for buffered exposed datapath architectures from dataflow graphsProceedings of the 23rd ACM SIGPLAN/SIGBED International Conference on Languages, Compilers, and Tools for Embedded Systems10.1145/3519941.3535076(133-145)Online publication date: 14-Jun-2022
  • (2019)Planar Graphs have Bounded Queue-Number2019 IEEE 60th Annual Symposium on Foundations of Computer Science (FOCS)10.1109/FOCS.2019.00056(862-875)Online publication date: Nov-2019

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