For integers m and n, where 2 m n and n 3, D (n, m) denotes the digraph obtained by reversing the direction of m - 1 consecutive arcs of a directed cycle of length n. Let D be an oriented graph of order p 3 with the minimum out-degree and in-degree at least p{/2} - 1. We introduce and study the following conjecture: for every 3 n p and 2 m n, D contains a D (n, m). In this paper, we show that if p 10 and m = 3, then this conjecture is true, i. e. , D contains a subdigraph obtained from a Hamiltonian cycle of D by reversing the direction of two consecutive arcs. We present examples of oriented graphs showing that this result is sharp in the following sense: both lower bounds p{/2} - 1 and 10 are tight. We also suggest some conjectures and problems.
Samvel Darbinyan (Mon,) studied this question.