We consider the problem of coloring a unit interval graph dynamically. Intervals arrive one after the other and have to be colored immediately such that no two intervals of the same color overlap. In each step, only a limited number of intervals may be recolored to maintain a proper coloring (thus interpolating between the well-studied online and offline settings). The number of allowed recolorings per step is the so-called recourse budget. In addition, I will discuss issues related to the chromatic number of unit circular arc graphs, which are closely related to the above problem.
This is joint work with Anna Zych-Pawlewicz.