  In the online graph coloring problem, vertices from a graph G, known in
advance, arrive in an online fashion and an algorithm must immediately assign a
color to each incoming vertex v so that the revealed graph is properly colored.
The exact location of v in the graph G is not known to the algorithm. The
online chromatic number of G is the smallest number of colors such that some
online algorithm is able to properly color G for any incoming order. We prove
that computing the online chromatic number of a graph is PSPACE-complete.
