A Hamilton Cycle in the k-Sided Pancake Network

We present a Hamilton cycle in the k-sided pancake network and four combinatorial algorithms to traverse cycle. The network’s vertices are coloured permutations $$\pi = p_1p_2\cdots p_n$$ , where each $$p_i$$ has an associated colour $$\{0,1,\ldots k\,-\,1\}$$ . There is directed edge $$(\pi _1,\pi _2)$$ if _2$$ can be obtained from _1$$ by “flip” of length j, which reverses first j elements increments their modulo k. Our particular created using greedy min-flip strategy, average flip edges we use bounded constant. By reinterpreting order recursively, generate successive O(1)-amortized time, or loop-free algorithm. also show how compute successor any permutation O(n)-time. construction generalizes known cycles for (where $$k=1$$ ) burnt $$k=2$$ ). Interestingly, max-flip strategy works on networks, but it does not work when $$k>2$$