BYPATHS IN TOURNAMENTS

If every are of a 3-connected tournament T is contained in a cycle of length 3, then every are of T has a bypath of length k for each k grea ter than or equal to 3, unless T is isomorphic to two tournaments, eac h of which has exactly 8 vertices. This extends the corresponding resu lt for regular tournaments, due to Alspach, Reid and Roselle (1974).