5-choosability of graphs with crossings far apart
  We give a new proof of the fact that every planar graph is 5-choosable, and use it to show that every graph drawn in the plane so that the distance between every pair of crossings is at least 15 is 5-choosable. At the same time we may allow some vertices to have lists of size four only, as long as they are far apart and far from the crossings. 
Zdenek Dvorak, Bernard Lidicky, Bojan Mohar
math.CO