Let
be an integer with
≥ 2. A digraph is
-quasi-transitive, if for any path
...
of length
,
and
are adjacent. Let
be a strong
-quasi-transitive digraph with even
≥ 4 and diameter at least
+2. It has been shown that
has a Hamiltonian path. However, the Hamiltonian cycle problem in
is still open. In this paper, we shall show that
may contain no Hamiltonian cycle with
≥ 6 and give the sufficient condition for
to be Hamiltonian.
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