  A collection of graphs is \textit{nearly disjoint} if every pair of them
intersects in at most one vertex. We prove that if $G_1, \dots, G_m$ are nearly
disjoint graphs of maximum degree at most $D$, then the following holds. For
every fixed $C$, if each vertex $v \in \bigcup_{i=1}^m V(G_i)$ is contained in
at most $C$ of the graphs $G_1, \dots, G_m$, then the (list) chromatic number
of $\bigcup_{i=1}^m G_i$ is at most $D + o(D)$. This result confirms a special
case of a conjecture of Vu and generalizes Kahn's bound on the list chromatic
index of linear uniform hypergraphs of bounded maximum degree. In fact, this
result holds for the correspondence (or DP) chromatic number and thus implies a
recent result of Molloy, and we derive this result from a more general list
coloring result in the setting of `color degrees' that also implies a result of
Reed and Sudakov.
