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arXiv · 2008.10336

Lazy Queue Layouts of Posets

Jawaherul Md. Alam·Michael A. Bekos·Martin Gronemann·Michael Kaufmann·Sergey Pupyrev
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Abstract

We investigate the queue number of posets in terms of their width, that is, the maximum number of pairwise incomparable elements. A long-standing conjecture of Heath and Pemmaraju asserts that every poset of width w has queue number at most w. The conjecture has been confirmed for posets of width w=2 via so-called lazy linear extension. We extend and thoroughly analyze lazy linear extensions for posets of width w > 2. Our analysis implies an upper bound of $(w-1)^2 +1$ on the queue number of width-w posets, which is tight for the strategy and yields an improvement over the previously best-known bound. Further, we provide an example of a poset that requires at least w+1 queues in every linear extension, thereby disproving the conjecture for posets of width w > 2.

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Jawaherul Md. Alam, Michael A. Bekos, Martin Gronemann, Michael Kaufmann, Sergey Pupyrev. 2020-08-24. Lazy Queue Layouts of Posets. https://arxiv.org/abs/2008.10336

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