An Eulerian circuit in a directed graph is one of the most fundamental Graph Theory notions. Detecting if G has unique can be done polynomial time via BEST theorem by de Bruijn, van Aardenne-Ehrenfest, Smith and Tutte (1941–1951) [15], [16] (involving counting arborescences), or tailored characterization Pevzner, 1989 computing intersection simple cycles G), both which thus rely on overly compl...