A graph is $k$-planar if it can be drawn in the plane so that each edge is crossed at most $k$ times. Typically, the class of 1-planar graphs is among the most investigated graph families within the so-called “beyond planar graphs”. A dynamic $\ell$-list coloring of a graph is a proper coloring so that each vertex receives a color from a list of $\ell$ distinct candidate colors assigned to it, and meanwhile, there are at least two colors appearing in the neighborhood of every vertex of degree at least two. In this paper, we prove that each 1-planar graph has a dynamic 11-list coloring. Moreover, we show a relationship between the dynamic coloring of 1-planar graphs and the proper coloring of 2-planar graphs, which states that the dynamic (list) chromatic number of the class of 1-planar graphs is at least the (list) chromatic number of the class of 2-planar graphs.

图是 $ķ$-平面（如果可以在平面上绘制），以便每个边缘最多交叉 $ķ$次。通常，一平面图的类别属于所谓的“超越平面图”中研究最多的图族。动态的$\ell$图的列表着色是一种适当的着色，因此每个顶点都可以从 $\ell$不同的候选颜色分配给它，同时，在至少两个度数的顶点附近至少出现两种颜色。在本文中，我们证明了每个1平面图都具有动态的11列表着色。此外，我们显示了1平面图的动态着色与2平面图的正确着色之间的关系，这表明1平面图的类的动态（列表）色数至少为（列表） 2平面图类的色数。