Abstract
Let D be a strong digraph on n ≥ 4 vertices. In [3, Discrete Applied Math., 95 (1999) 77–87)], J. Bang-Jensen, Y. Guo and A. Yeo proved the following theorem: if (∗) d{x) + d(y) ≥ 2n−l and min{d+(x) + d− (y), d−(x)+d+(y)} ≥ n−1 for every pair of non-adjacent vertices x, y with a common in-neighbour or a common out-neighbour, then D is hamiltonian. In this note we show that: if D is not directed cycle and satisfies the condition (∗), then D contains a cycle of length n − 1 or n − 2.