A Hamilton Cycle in the k-Sided Pancake Network

03/16/2021

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by   Ben Cameron, et al.

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We present a Hamilton cycle in the k-sided pancake network and four combinatorial algorithms to traverse the cycle. The network's vertices are coloured permutations π = p_1p_2⋯ p_n, where each p_i has an associated colour in {0,1,…, k-1}. There is a directed edge (π_1,π_2) if π_2 can be obtained from π_1 by a "flip" of length j, which reverses the first j elements and increments their colour modulo k. Our particular cycle is created using a greedy min-flip strategy, and the average flip length of the edges we use is bounded by a constant.