Reconstructibility of the Kr-count from n − 1 cards

The Reconstruction Conjecture of Kelly and Ulam states that any graph G with n≥3 vertices can be reconstructed from the multiset D(G) of unlabelled subgraphs G−v for all v∈V(G). We refer to D(G) as the deck of G and G−v∈D(G) as the cards of G. This was posed in the 1940s and is still wide open today. In an effort to understand reconstructibility better, a growing collection of research is concerned with understanding what properties of G can be reconstructed from a (potentially adversarially chosen) collection of k cards for some k更多