  We study the addition of N_f flavor D5-branes to supergravity solutions
describing D5-branes wrapping two-cycles of genus g>1 inside a six-dimensional
space equipped with an SU(3)-structure. The non-zero genus g on the gravity
side is dual to the existence of massless adjoint chiral superfields. Three
types of internal manifolds are considered, each involving one of the following
fibered products: H_2 x SL_2, S^2 x SL_2 or H_2 x S^3, where SL_2 stands for
the universal cover of SL(2,R). For the first one, we investigate the dual
field theories. We show that some of the solutions with N_f non-zero are dual
to four-dimensional N = 1 field theories exhibiting a Kutasov-like duality
taking N_c to k N_f - N_c, and keeping N_f fixed. Computed from the
supergravity picture, k is in general a rational number, which can be made
integer to fit the expectation from the field theory side. We finally study
some other properties of those field theories.
