Dimension is polynomial in height for posets with planar cover graphs

Jakub Kozik, Piotr Micek, William T. Trotter

We show that height $h$ posets that have planar cover graphs have dimension $\mathcal{O}(h^6)$. Previously, the best upper bound was $2^{\mathcal{O}(h^3)}$. Planarity plays a key r…