Strict queue numbers of hypercube and folded hypercube

The strict queue number measures the minimum resources required for a strict non-overlapping layout and is also useful for deriving bounds on the queue numbers of cartesian products and several other graph products. By applying this parameter, Gregor et al. established that qn⁡(Qn)≤n−⌊log2⁡n⌋. For folded hypercubes, Geng et al. proved that qn⁡(FQn)≤2n−2, and this bound was later improved by Pai to qn⁡(FQn)≤n. In this paper, we partition the edges of the n-dimensional hypercube Qn (n≥1) into n strict queues under the vertex ordering proposed by Geng et al., and obtain that sqn⁡(Qn)=n. Based on this result, we further prove that sqn⁡(FQn)=n+1 for the n-dimensional folded hypercube FQn (n≥2).