Compatible Eulerian circuits in \(K_ n^{**}\) (Q1842648)

Let \(G\) be an Eulerian digraph. Two Euler tours of \(G\) are compatible if no two arcs of \(G\) are consecutive in both tours. It is proved that if \(G\) is a complete symmetric digraph of order \(n\), then \(G\) has \(\varphi(n)\) pairwise compatible Euler tours, where \(\varphi\) denotes the Euler function.