Classical reconstruction from (n−1)-vertex induced subgraphs (Kelly–Ulam type)

Determine whether every undirected n-vertex graph is uniquely determined, up to isomorphism, by the multiset of its induced subgraphs on n−1 vertices.

Background

As background motivation, the paper recalls the classical graph reconstruction problem from structural graph theory: reconstructing an n-vertex graph from its deck of (n−1)-vertex induced subgraphs.

Despite substantial paper, whether arbitrary graphs are reconstructible from their (n−1)-vertex decks remains unresolved.