Long Cycles in the Middle Two Levels of the Boolean Lattice

An intriguing open question is whether the graph formed by the middle two levels of the Boolean lattice of subsets of a k element set has a Hamilton path for all k We consider nding a lower bound on the length of the longest cycle in this graph A result of Babai for vertex transitive graphs gives a lower bound of N where N is the total number of vertices in the middle two levels In this paper we show how to construct a cycle of length N c where c