The reconstruction conjecture for finite simple graphs

Let $G$ be a finite simple undirected graph. For each vertex $v\in V(G)$, let $G_v=[G-v]_{\cong}$ be its card, and let

$$\mathcal{D}(G)=\{\!\{G_v:v\in V(G)\}\!\}$$

be its deck. The graph $G$ is reconstructible if every graph $H$ with $\mathcal{D}(H)=\mathcal{D}(G)$ is isomorphic to $G$. The reconstruction conjecture. Every graph of order at least $3$ is reconstructible. This is one of the central open problems in structural graph theory, asserting that a graph is determined up to isomorphism by the multiset of its vertex-deleted induced subgraphs. The conjecture remains wide open, although the paper proves it for interval graphs with at least three vertices.