Computing the Bandwidth of Interval Graphs

In this note, an $O ( | V |k )$ algorithm is described for determining whether an interval graph on $| V |$ vertices has a bandwidth less than or equal to a given integer $k$. While the algorithm is not the first to resolve this problem, it does admit a shorter proof of its correctness than a previous algorithm of the same complexity due to Kratsch (Information and Computation, 74 (1987), pp. 140