The Graph Reconstruction Conjecture claims that any simple graph with 3 or more vertices is reconstructible from its "deck" of vertex-deleted subgraphs. (A nice introduction to this problem is at this Wikipedia page.)

My general question: I would be interested in *any* recent progress on the conjecture. The sources in the Wikipedia article seem to be quite old. (I also have a copy of a Bondy and Hemminger survey from 1977. A more recent article by Ramachandran (in pdf here) is from 2004 but like many works on this conjecture, quickly detours into other reconstruction questions, edge reconstruction, etc.)

A more specific question: since one can reconstruct the degree sequence of a graph then any regular graph can be reconstructed. But graphs with exactly two degrees, $k$ and $k-1$, seem to be quite hard to reconstruct. I would be *especially interested* in results related to graphs with exactly two degrees, $k$ and $k-1.$

Even more narrowly, can we reconstruct graphs in which all vertices have degree 2 or 3? (Apparently Kocay worked on that in the early 1980s, says Ramachandran.) Surely "small" graphs of degrees {2,3} are accessible to modern computers so there may now be a place for fertile exploration on this problem?