  Let $G$ be a graph with vertex set $V$ and let $g, f : V\rightarrow
\mathbb{Z}^+$ be two functions such that $g\le f$. We say that $G$ has all $(g,
f )$-factors if $G$ has an $h$-factor for every $h: V\rightarrow \mathbb{Z}^+$
such that $g(v)\le h(v)\le f (v)$ for every $v\in V$ and
$\sum_{v\in{V}}h(v)\equiv 0\pmod 2$. Two decades ago, Niessen derived from
Tutte's $f$-factor theorem a similar characterization for the property of
graphs having all $(g, f )$-factors and asked whether there is a polynomial
time algorithm for testing whether a graph $G$ has all $(g, f )$-factors (A
characterization of graphs having all $(g, f )$-Factors, \emph{J. Combin.
Theory, Ser. B}, \textbf{72} (1998), 152--156). In this paper, we show that it
is NP-hard to determine whether a graph $G$ has all $(g,f)$-factors, which
gives a negative answer to the question of Niessen.
