  We present an algorithm for updating the Reeb graph under fully dynamic
changes of the function values. The basic event is the interchange of two
consecutive vertex values. The algorithm updates the Reeb graph in $O(l g{n})$
worst-case deterministic time for each such interchange, where $l$ is an upper
bound on the size of the star of the involved vertices, and g(n) is a
worst-case bound for the dynamic graph connectivity problem. Moreover, we argue
that $O(l)$ is a lower bound for this operation in general.
