Hamiltonicity of digraphs for universal cycles of permutations

The digraphs P(n, k) have vertices corresponding to length k permutations of an n set and arcs corresponding to (k + 1) permutations. Answering a question of Starling, Klerlein, Kier and Carr we show that these digraphs are Hamiltonian for k n - 3. We do this using restricted Eulerian cycles and the fact that P(n, k) is nearly the line digraph of P(n, k -1). We also show that the digraphs P(n, n-2) are not Hamiltonian for n 4 using a result of Rankin on Cayley digraphs.

• Type: Journal
• Year: 2006
• Where: EJC
• Authors: Garth Isaak
• Keywords: Cayley Digraphs, EJC 2006, EJC 2007, Permutations, Starling