  Not every graph has an Eulerian tour. But every finite, strongly connected
graph has a multi-Eulerian tour, which we define as a closed path that uses
each directed edge at least once, and uses edges e and f the same number of
times whenever tail(e)=tail(f). This definition leads to a simple
generalization of the BEST Theorem. We then show that the minimal length of a
multi-Eulerian tour is bounded in terms of the Pham index, a measure of
'Eulerianness'.
