  It is well known that if $G = (V, E)$} is a multigraph and $X\subset V$ is a
subset of even order, then $G$ contains a spanning forest $H$ such that each
vertex from $X$ has an odd degree in $H$ and all the other vertices have an
even degree in $H$. This spanning forest may have isolated vertices. If this is
not allowed in $H$, then the situation is much more complicated. In this paper,
we study this problem and generalize the concepts of even-factors and
odd-factors in a unified form.
