On a cyclic connectivity property of directed graphs Original Research Article

Let us call a digraph D cycle-connected if for every pair of vertices image there exists a cycle containing both u and image. In this paper we study the following open problem introduced by Ádám. Let D be a cycle-connected digraph. Does there exist a universal edge in D, i.e., an edge image such that for every image there exists a cycle C such that image and image? In his 2001 paper Hetyei conjectured that cycle-connectivity always implies the existence of a universal edge. In the present paper we prove the conjecture of Hetyei for bitournaments.