Online Interval Coloring and Variants

We study interval coloring problems and present new upper and lower bounds for several variants. We are interested in four problems, online coloring of intervals with and without bandwidth and a new problem called lazy online coloring again with and without bandwidth. We consider both general interval graphs and unit interval graphs. Specifically, we establish the difference between the two main problems which are interval coloring with and without bandwidth. We present the first non-trivial lower bound of 3.2609 for the problem with bandwidth. This improves the lower bound of 3 that follows from the tight results for interval coloring without bandwidth presented in [9].