Dichotomy for hypergraph edge-deletion complexity

Prove that for every k ≥ 3 and every k-uniform hypergraph F, computing rem_F(G), the minimum number of edges whose deletion makes an input k-uniform hypergraph G F-free, is polynomial-time solvable when F is a matching and NP-hard otherwise.

Background

The paper proposes a complexity dichotomy for forbidden k-uniform hypergraphs with k ≥ 3. A matching is shown to define a polynomial-time solvable edge-deletion problem in Theorem 1.4, establishing the positive part of the conjecture. The negative part remains unresolved in full generality: the paper proves NP-hardness for the minimally non-matching configurations consisting of two k-edges intersecting in t vertices, but does not establish NP-hardness for every other k-graph F.