  The Near-Bipartiteness problem is that of deciding whether or not the
vertices of a graph can be partitioned into sets $A$ and $B$, where $A$ is an
independent set and $B$ induces a forest. The set $A$ in such a partition is
said to be an independent feedback vertex set. Yang and Yuan proved that
Near-Bipartiteness is polynomial-time solvable for graphs of diameter 2 and
NP-complete for graphs of diameter 4. We show that Near-Bipartiteness is
NP-complete for graphs of diameter 3, resolving their open problem. We also
generalise their result for diameter 2 by proving that even the problem of
computing a minimum independent feedback vertex is polynomial-time solvable for
graphs of diameter 2.
