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Queue layouts of hypercubes

By Petr Gregor, Riste Skrekovski and Vida Vukasinovic


A queue layout of a graph consists of a linear ordering σ of its vertices, and a partition of its edges into sets, called queues, such that in each set no two edges are nested with respect to σ. We show that the n-dimensional hypercube Qn has a layout into n−⌊log2 n⌋ queues for all n ≥ 1. On the other hand, for every ε> 0 every queue layout of Qn has more than ( 1 2 − ε)n − O(1/ε) queues, and in particular, more than (n − 2)/3 queues. This improves previously known upper and lower bounds on the minimal number of queues in a queue layout of Qn. For the lower bound we employ a new technique of out-in representations and contractions which may be of independent interest

Topics: Key words. queue layout, queue-number, hypercube
Year: 2011
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