Independent Even Cycles in the Pancake Graph and Greedy Prefix-Reversal Gray Codes

Any `–cycle, 6 6 `6 n!, can be embedded in the Pancake graph Pn, n > 3. In this paper we prove the existence of a family of maximal sets of even independent cycles with length bounded by O(n2). We introduce the new concept of Prefix– reversal Gray codes based on the independent cycles which extends the known greedy Prefix–reversal Gray code constructions considered by Zaks and Williams. We derive the cases of non-existence of such codes using the fastening cycle approach. Along with that we give necessary condition for the existence of greedy Prefix–reversal Gray codes in the graph.