  A graph is 2-degenerate if every subgraph contains a vertex of degree at most
2. We show that every 2-degenerate graph can be drawn with straight lines such
that the drawing decomposes into 4 plane forests. Therefore, the geometric
arboricity, and hence the geometric thickness, of 2-degenerate graphs is at
most 4. On the other hand, we show that there are 2-degenerate graphs that do
not admit any straight-line drawing with a decomposition of the edge set into 2
plane graphs. That is, there are 2-degenerate graphs with geometric thickness,
and hence geometric arboricity, at least 3. This answers two questions posed by
Eppstein [Separating thickness from geometric thickness. In Towards a Theory of
Geometric Graphs, vol. 342 of Contemp. Math., AMS, 2004].
