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.Comment: 14 pages, 10 figures, Appears in the Proceedings of the 26th
International Symposium on Graph Drawing and Network Visualization (GD 2018