# The Queue-Number of Posets of Bounded Width or Height

1 ACRO - Algorithmique, Combinatoire et Recherche Opérationnelle
LIS - Laboratoire d'Informatique et Systèmes
2 Algorithmics Research Group
UJ - Jagiellonian University [Krakow]
Abstract : Heath and Pemmaraju conjectured that the queue-number of a poset is bounded by its width and if the poset is planar then also by its height. We show that there are planar posets whose queue-number is larger than their height, refuting the second conjecture. On the other hand, we show that any poset of width $2$ has queue-number at most $2$, thus confirming the first conjecture in the first non-trivial case. Moreover, we improve the previously best known bounds and show that planar posets of width $w$ have queue-number at most $3w-2$ while any planar poset with $0$ and $1$ has queue-number at most its width.
Document type :
Book sections
Domain :

https://hal.archives-ouvertes.fr/hal-02068620
Contributor : Kolja Knauer <>
Submitted on : Friday, March 15, 2019 - 10:17:35 AM
Last modification on : Monday, May 11, 2020 - 11:00:11 AM

### Citation

Kolja Knauer, Piotr Micek, Torsten Ueckerdt. The Queue-Number of Posets of Bounded Width or Height. International Symposium on Graph Drawing and Network Visualization GD 2018: Graph Drawing and Network Visualization, 2018, ⟨10.1007/978-3-030-04414-5_14⟩. ⟨hal-02068620⟩

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