  An edge-coloring of a graph $G$ with colors $1,\ldots,t$ is an \emph{interval
$t$-coloring} if all colors are used, and the colors of edges incident to each
vertex of $G$ are distinct and form an integer interval. It is well-known that
there are graphs that do not have interval colorings. The \emph{deficiency} of
a graph $G$, denoted by $\mathrm{def}(G)$, is the minimum number of pendant
edges whose attachment to $G$ leads to a graph admitting an interval coloring.
In this paper we investigate the problem of determining or bounding of the
deficiency of complete multipartite graphs. In particular, we obtain a tight
upper bound for the deficiency of complete multipartite graphs. We also
determine or bound the deficiency for some classes of complete multipartite
graphs.
