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We study relations between the unknotting number and the crossing number of a spatial embedding of a handcuff-graph and a theta curve. It is well known that for any non-trivial knot [Formula: see text] twice the unknotting number of [Formula: see text] is less than or equal to the crossing number of [Formula: see text] minus one. We show that this is extended to handlebody-knots. We also characterize the handlebody-knots which satisfy the equality.

On inequalities between unknotting numbers and crossing numbers of spatial embeddings of trivializable graphs and handlebody-knots