9 problems

For a graph $G$, a queue layout is a linear ordering of $V(G)$ together with a partition of $E(G)$ into queues such that no two edges in the same queue are nested; the queue-number…

Let $T$ be the infinite rooted binary tree, and let $\operatorname{Aut}(T)$ be its group of root- and parent-preserving automorphisms. The source proves that…

A group may be considered with respect to queue number, with the uniform version requiring one bound that works uniformly for the relevant group actions. The source establishes fin…

Let $P$ be a poset, and let its width be the maximum number of pairwise incomparable elements. The queue-number of $P$ is the least number of queues in a queue layout based on a li…

A poset $P$ is a partially ordered set; its height is the maximum number of pairwise comparable elements. The cover graph $G_P$ has vertex set $P$ and an edge for each covering rel…

A planar graph is a graph that can be drawn in the plane with no crossing edges. The unbounded queue-number conjecture. Planar graphs should have unbounded queue-number. This conje…

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…

Let $P$ be a poset, let $\operatorname{width}(P)$ be the maximum size of an antichain, and let ${\operatorname{qn}}(P)$ denote its queue-number. Write $w=\operatorname{width}(P)$.…