  Given a nonnegative integer weight $f(v)$ for each vertex $v$ in a multigraph
$G$, an {\it $f$-bounded subgraph} of $G$ is a multigraph $H$ contained in $G$
such that $d_H(v)\le f(v)$ for all $v\in V(G)$. Using Tutte's $f$-Factor
Theorem, we give a new proof of the min-max relation for the maximum size of an
$f$-bounded subgraph of $G$. When $f(v)=1$ for all $v$, the formula reduces to
the classical Tutte--Berge Formula for the maximum size of a matching.
