Abstract
The vertex-arboricity a(G) of a graph G is the minimum number of colors required to color the vertices of G such that no cycle is monochromatic. The list vertex-arboricity al(G) of G is the list-coloring version of this invariant. It was known that every planar graph G has al(G)≤3. In this paper, we extend this result by showing that every graph G drawn in the plane so that the distance between every pair of crossings is at least 2 has al(G)≤3.
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