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) there exists a cycle containing both u and v. 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 inD, i.e., an edge e ∈ E(D) such that for everyw ∈ V (D) there exists a cycle C such thatw ∈ V (C) and 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. Published by Elsevier B.V.