Queue Layouts of Two-Dimensional Posets

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