  1-planar graphs are graphs that can be drawn in the plane such that any edge
intersects with at most one other edge. Ackerman showed that the edges of a
1-planar graph can be partitioned into a planar graph and a forest, and claims
that the proof leads to a linear time algorithm. However, it is not clear how
one would obtain such an algorithm from his proof. In this paper, we first
reprove Ackerman's result (in fact, we prove a slightly more general statement)
and then show that the split can be found in linear time by using an
edge-contraction data structure by Holm et al.
