Abstract :
The Reconstruction Conjecture asserts that every finite simple undirected graph on 3 or more vertices is determined, up to isomorphism, by its collection of (unlabeled) one-vertex-deleted subgraphs. A more general problem can be investigated if the collection consists of all (unlabeled) subgraphs with a restricted number of vertices. Kelly (Pacific J. Math. 7 (1957) 961–968) first raised the possibility of deleting several points from a graph and Manvel (Discrete Math. 8 (1974) 181–185) offered some basic observations on the problem. Here, we propose a review on the progress made in the last 25 years. Also, discussing the class of all finite trees, we go back to the original Kellyʹs interest.
