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Planar posets have dimension at most linear in their height
Published 22 Dec 2016 in math.CO and cs.DM | (1612.07540v2)
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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