Queue Layouts of Two-Dimensional Posets

08/26/2022

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by   Sergey Pupyrev, et al.

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The queue number of a poset is the queue number of its cover graph when the vertex order is a linear extension of the poset. Heath and Pemmaraju conjectured that every poset of width w has queue number at most w. The conjecture has been confirmed for posets of width w=2 and for planar posets with 0 and 1. In contrast, the conjecture has been refused by a family of general (non-planar) posets of width w>2. In this paper, we study queue layouts of two-dimensional posets. First, we construct a two-dimensional poset of width w > 2 with queue number 2(w - 1), thereby disproving the conjecture for two-dimensional posets. Second, we show an upper bound of w(w+1)/2 on the queue number of such posets, thus improving the previously best-known bound of (w-1)^2+1 for every w > 3.