COMPATIBLE EULERIAN CIRCUITS IN K-N

Let K-n* be the complete symmetric digraph with a loop at each vertex . We say that two K-n* are compatible if no pair of arcs of the digra ph are consecutive in both eulerian circuits. We prove that there exis t phi(n) pairwise compatible eulerian circuits in K-n*, where phi den otes the Euler function, and we give an effective construction of thes e circuits.