Dimension is polynomial in height for posets with planar cover graphs
Combinatorics
2022-10-13 v3 Discrete Mathematics
Abstract
We show that height posets that have planar cover graphs have dimension . Previously, the best upper bound was . Planarity plays a key role in our arguments, since there are posets such that (1) dimension is exponential in height and (2) the cover graph excludes as a minor.
Cite
@article{arxiv.1907.00380,
title = {Dimension is polynomial in height for posets with planar cover graphs},
author = {Jakub Kozik and Piotr Micek and William T. Trotter},
journal= {arXiv preprint arXiv:1907.00380},
year = {2022}
}