4 research outputs found
The Queue-Number of Posets of Bounded Width or Height
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 has queue-number at most , 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 have queue-number at most
while any planar poset with and 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
The Queue-Number of Posets of Bounded Width or Height
14 pages, 10 figures, Appears in the Proceedings of the 26th International Symposium on Graph Drawing and Network Visualization (GD 2018)International audienceHeath 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 has queue-number at most , 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 have queue-number at most while any planar poset with and has queue-number at most its width