On a cyclic connectivity property of directed graphs

Let us call a digraph D   cycle-connected if for every pair of vertices u,v∈V(D)u,v∈V(D) there exists a cycle containing both u   and vv. 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 e∈E(D)e∈E(D) such that for every w∈V(D)w∈V(D) there exists a cycle C   such that w∈V(C)w∈V(C) and e∈E(C)e∈E(C)?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.