Queue layouts on folded hypercubes

Abstract

A queue layout of a graph $G$ consists of a linear order of its vertices, and a partition of its edges into queues, such that no two edges in the same queue are nested. The queue number $qn\left(G\right)$ is the minimum number of queues required in a queue layout of $G$. A graph $G$ is a $q$-queue graph if $qn\left(G\right)\le q$. Gregor et al. in Gregor et al. (2012) showed that the $n$-dimensional hypercube $Q_n$ has a layout into $n-\lfloor {log}_{2}n\rfloor$ queues for all $n\ge 1$. Pai et al. in Pai et al. (0000) gave several upper bounds when $n\le 7$. In particular, $qn\left(F{Q}_7\right)\le 12$. In this work, we generally obtain that $F{Q}_n$ has queue number at most $2n-2$ for all $n\ge 2$.