Planar Posets Have Dimension at Most Linear in Their Height

Abstract

We prove that every planar poset $P$ of height $h$ has dimension at most $192h + 96$. 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 $h$ and dimension at least $(4/3)h-2$.

Locations

• SIAM Journal on Discrete Mathematics - View
• arXiv (Cornell University) - View - PDF
• DataCite API - View