Planar posets have dimension at most linear in their height
Combinatorics
2018-01-11 v2 Discrete Mathematics
Abstract
We prove that every planar poset of height has dimension at most . This improves on previous exponential bounds and is best possible up to a constant factor. We complement this result with a construction of planar posets of height and dimension at least .
Cite
@article{arxiv.1612.07540,
title = {Planar posets have dimension at most linear in their height},
author = {Gwenaël Joret and Piotr Micek and Veit Wiechert},
journal= {arXiv preprint arXiv:1612.07540},
year = {2018}
}
Comments
v2: Minor changes