Recognizing random intersection graphs (Q1587611)

For a hypergraph \(H=(V,E)\) the \(l\)-intersection graph \(\Omega_l(H)\) has the vertex set \(E\) and two of its vertices are adjacent if the corresponding edges of \(H\) have at least \(l\) common elements. The author designs a polynomial-time algorithm that reconstructs a simple \(k\)-uniform hypergraph from its \(l\)-intersection graph for a class of random \(k\)-uniform hypergraphs. He also presents two algorithms for reconstructing almost every random graph from its related hypergraphs.