A new lower bound for the on-line coloring of intervals with bandwidth

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 asymptotic competitive ratio for the on-line coloring of intervals with bandwidth which improves the best known lower bound of 247. For the on-line coloring of unit intervals with bandwidth we improve the lower bound of 1.831 to 2.