Cycles in folded hypercubes

This work investigates important properties related to cycles of embedding into the folded hypercube FQn for n≥2n≥2. The authors observe that FQn is bipartite if and only if nn is odd, and show that the minimum length of odd cycles is n+1n+1 if nn is even. The authors further show that every edge of FQn lies on a cycle of every even length from 4 to 2n2n; if nn is even, every edge of FQn also lies on a cycle of every odd length from n+1n+1 to 2n−12n−1.