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arXiv · 1612.07540

Planar posets have dimension at most linear in their height

Gwenaël Joret·Piotr Micek·Veit Wiechert
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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 $(4/3)h-2$.

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Gwenaël Joret, Piotr Micek, Veit Wiechert. 2017-09-23. Planar posets have dimension at most linear in their height. https://doi.org/10.1137/17m111300x

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