2 problems

Let $P$ be a planar poset on $n$ elements, and let ${\operatorname{qn}}(P)$ denote its queue-number. Heath–Pemmaraju's square-root conjecture. Every planar poset on $n$ elements ha…

Let $P$ be a planar poset, meaning that it admits a crossing-free diagram, and let $h$ be its height, the maximum size of a chain. Let ${\operatorname{qn}}(P)$ denote its queue-num…