  The on-line interval coloring and its variants are important combinatorial
problems with many applications in network multiplexing, resource allocation
and job scheduling. In this paper we present a new lower bound of $4.1626$ for
the competitive ratio for the on-line coloring of intervals with bandwidth
which improves the best known lower bound of $\frac{24}{7}$. For the on-line
coloring of unit intervals with bandwidth we improve the lower bound of $1.831$
to $2$.
