Multi-Eulerian tours of directed graphs (Q281626)

Summary: 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 \(\operatorname{tail}(e)=\operatorname{tail}(f)\). 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'.