  Albertson and Berman conjectured that every planar graph has an induced
forest on half of its vertices. The best known lower bound, due to Borodin, is
that every planar graph has an induced forest on two fifths of its vertices. In
a related result, Chartran and Kronk, proved that the vertices of every planar
graph can be partitioned into three sets, each of which induce a forest.
  We show tighter results for 2-outerplanar graphs. We show that every
2-outerplanar graph has an induced forest on at least half the vertices by
showing that its vertices can be partitioned into two sets, each of which
induces a forest. We also show that every 2-outerplanar graph has an induced
outerplanar graph on at least two-thirds of its vertices.
