k-edge reconstruction conjecture for finite graphs

Determine whether every finite graph with n ≥ k + 3 edges is uniquely determined up to isomorphism by its k-edge deck ED_k(G), defined as the multiset of all subgraphs obtained by deleting k edges from G.

Background

The k-edge deck generalizes the standard edge deck by deleting k edges at a time. The conjecture posits that sufficiently many edges (n ≥ k + 3) guarantee unique reconstruction from ED_k(G).

The authors note that their K-theoretic reformulation of the edge reconstruction conjecture extends to this k-edge setting by replacing n−1 with n−k throughout their construction.