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Heath and Pemmaraju [9] 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.

The Queue-Number of Posets of Bounded Width or Height