The Easiest Unsolved Problem in Graph Theory

Our new blog post about reconstruction conjecture, a well-known graph theory problem with 80 years of results but no final proof yet. I have already written several posts in this channel about it and it to me it's one of the grand challenges in graph theory (along with graph isomorphism problem). It seems there is quite some progress, so I hope to see it being resolved during my lifetime. In the meantime, we considered graph families for which reconstruction conjecture is known to be true and tried to come up with the easiest family of graphs that is still not resolved and have very few vertices. The resulted family is a type of bidegreed graphs (close to regular) on 20 vertices, which is probably possible to verify on the computer (though it would take a year or so).