  For a fixed positive integer $k$, a set $S$ of vertices of a graph or
multigraph is called a $k$-independent set if the subgraph induced by $S$ has
maximum degree less than $k$. The well-known algorithm MAX finds a maximal
$k$-independent set in a graph or multigraph by iteratively removing vertices
of maximum degree until what remains has maximum degree less than $k$. We give
an efficient procedure that determines, for a given degree sequence $D$, the
smallest cardinality $b(D)$ of a $k$-independent set that can result from any
application of MAX to any loopless multigraph with degree sequence $D$. This
analysis of the worst case is sharp for each degree sequence $D$ in that there
exists a multigraph $G$ with degree sequence $D$ such that some application of
MAX to $G$ will result in a $k$-independent set of cardinality exactly $b(D)$.
