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.

翻译：图的一个集合被称为\textit{近不交}若其中任意两个图至多相交于一个顶点。我们证明：若$G_1, \dots, G_m$是最大度不超过$D$的近不交图，则以下结论成立。对任意固定常数$C$，若每个顶点$v \in \bigcup_{i=1}^m V(G_i)$至多出现在$C$个图$G_1, \dots, G_m$中，则$\bigcup_{i=1}^m G_i$的（列表）色数不超过$D + o(D)$。该结果证实了Vu猜想的一个特例，并推广了Kahn关于有界最大度线性一致超图的列表边色数上界。事实上，该结果对对应（或DP）色数也成立，从而蕴含了Molloy近期的一个结果。我们从更一般的“色度”框架下的列表染色结论推导出该结果，该框架同时蕴含了Reed与Sudakov的结果。