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](http://en.wikipedia.org/wiki/Reconstruction_conjecture).)


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](http://onlinelibrary.wiley.com/doi/10.1002/jgt.3190010306/abstract) from 1977. A more recent article by Ramachandran [(in pdf here)](http://www.akcejournal.org/contents/vol1no1/Vol_1no_1-6.pdf) 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? 



Reconstructing graphs with vertices of degree $k$ and $k-1$
I have a paper on the Reconstruction Conjecture. It was published in an Elsevier journal dedicated to Discrete Mathematics. Its available online since 2007:



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> Kia Dalili, Sara Faridi and Will Traves. [Note: The Reconstruction Conjecture and edge ideals](http://dx.doi.org/10.1016/j.disc.2007.04.044). Discrete Mathematics 308(10), pp. 2002–2010, 2008. ([MathSciNet review](http://www.ams.org/mathscinet-getitem?mr=2394468))
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Just type Kia Dalili in the Author field for Search and it will show up.


