Queue Layouts of Two-Dimensional Posets
Abstract
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 $w > 3$.
- Publication:
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arXiv e-prints
- Pub Date:
- August 2022
- DOI:
- 10.48550/arXiv.2208.12802
- arXiv:
- arXiv:2208.12802
- Bibcode:
- 2022arXiv220812802P
- Keywords:
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- Mathematics - Combinatorics;
- Computer Science - Discrete Mathematics
- E-Print:
- Appears in the Proceedings of the 30th International Symposium on Graph Drawing and Network Visualization (GD 2022)