  We give improved algorithms for maintaining edge-orientations of a
fully-dynamic graph, such that the out-degree of each vertex is bounded. On one
hand, we show how to orient the edges such that the out-degree of each vertex
is proportional to the arboricity $\alpha$ of the graph, in a worst-case update
time of $O(\log^3 n \log \alpha)$. On the other hand, motivated by applications
including dynamic maximal matching, we obtain a different trade-off, namely the
improved worst case update time of $O(\log ^2 n \log \alpha)$ for the problem
of maintaining an edge-orientation with at most $O(\alpha + \log n)$ out-edges
per vertex. Since our algorithms have update times with worst-case guarantees,
the number of changes to the solution (i.e. the recourse) is naturally limited.
Our algorithms adapt to the current arboricity of the graph, and yield
improvements over previous work: Firstly, we obtain an
$O(\varepsilon^{-6}\log^3 n \log \rho)$ worst-case update time algorithm for
maintaining a $(1+\varepsilon)$ approximation of the maximum subgraph density,
$\rho$.
  Secondly, we obtain an $O(\varepsilon^{-6}\log^3 n \log \alpha)$ worst-case
update time algorithm for maintaining a $(1 + \varepsilon) \cdot OPT + 2$
approximation of the optimal out-orientation of a graph with adaptive
arboricity $\alpha$. This yields the first worst-case polylogarithmic dynamic
algorithm for decomposing into $O(\alpha)$ forests.Thirdly, we obtain
arboricity-adaptive fully-dynamic deterministic algorithms for a variety, of
problems including maximal matching, $\Delta+1$ coloring, and matrix vector
multiplication. All update times are worst-case $O(\alpha+\log^2n \log
\alpha)$, where $\alpha$ is the current arboricity of the graph.
