Graph Reconstruction Checker

The deck of G is the multiset {G-v₁, G-v₂, ..., G-vₙ}. Each 'card' is the graph obtained by deleting one vertex. The conjecture: the deck uniquely determines G (up to isomorphism) when n≥3.

K₁ and the empty graph on 1 vertex have the same deck (empty). K₂ and 2K₁ have the same deck ({K₁, K₁}). So n≤2 fails. For n≥3, no counterexample has been found in 80+ years.

Edge Reconstruction Conjecture: G (n≥4) is determined by its edge-deleted subgraphs {G-e : e∈E}. Also open! Proven for: n≥edges/2, dense graphs, many special classes. Harder than vertex version.