  We give an exact $O(nk^2)$ algorithm for finding the densest k subgraph in
outerplanar graphs. We extend this to an exact $O(nk^2 8^b)$ algorithm for
finding the densest k subgraph in b-outerplanar graphs. Finally, we hypothesize
that Baker's PTAS technique will not work for the densest k subgraph problem in
planar graphs.
