Bypasses in asymmetric digraphs

D. P. ROSELLE* Louisiana State University, Baton Rouge, Louisiana 70803 Communicated by W. T. Tutte Received September 7, 1973 A digraph G is said to be asymmetric if uv E G implies vu 4 G. If uv E G and P is a path of length k from IA to v, then P is called a k-bypass from u to v. In this paper we investigate asymmetric digraphs in which each line has a 2-bypass. Results are obtained on the existence of such digraphs, the relationship between Z-bypasses and longer bypasses, and the question of how prevalent such di- graphs are.