Graphs with two crossings are 5-choosable
  A graph G is k-choosable if G can be properly colored whenever every vertex has a list of at least k available colors. Thomassen's theorem states that every planar graph is 5-choosable. We extend the result by showing that every graph with at most two crossings is 5-choosable. 
Zden\v{e}k Dvo\v{r}\'ak, Bernard Lidick\'y, Riste \v{S}krekovski
math.CO