On the Queue-Number of Partial Orders

08/23/2021

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by   Stefan Felsner, et al.

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The queue-number of a poset is the queue-number of its cover graph viewed as a directed acyclic graph, i.e., when the vertex order must be a linear extension of the poset. Heath and Pemmaraju conjectured that every poset of width w has queue-number at most w. Recently, Alam et al. constructed posets of width w with queue-number w+1. Our contribution is a construction of posets with width w with queue-number Ω(w^2). This asymptotically matches the known upper bound.