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Planar posets have dimension at most linear in their height

par Joret, Gwenaël ;Micek, Piotr;Wiechert, Veit
Référence SIAM journal on discrete mathematics, 31, 4, page (2754-2790)
Publication Publié, 2017

Article révisé par les pairs

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Résumé :

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.