On an Extension of the Ghouila-Houri Theorem - Darbinyan, Samvel Kh. (Изд-во НАН РА)
Let D be a 2-strong digraph of order n ≥ 8 such that for every vertex x ∈ V(D)\{z}, d(x) ≥ n and d(z) ≥ n − 4, where z is a vertex in V(D). We prove that: If D contains a cycle passing through z of length equal to n − 2, then D is Hamiltonian. We also give a new sufficient condition for a digraph to be Hamiltonian-connected.
Keywords: Mathematical cybernetics; Computer science