More non-reconstructible hypergraphs

Abstract A k-hypergraph G consists of a vertex-set V ( G ) and an edge-set E ( G ), a set of k -subsets of V ( G ). If X ⊆ V ( G ), the edges of the induced subgraph G [ X ] are those edges of G whose vertices are all contained in X . If v ϵ V ( G ), then G - v denotes the induced subgraph G [ V ( G ) - v ]. Hypergraphs G and H are hypomorphic if there is a bijection o : V ( G )→ V ( H ) such that G - v ≅ H - o ( v ), for all v ϵ V ( G ). G and H are said to be reconstructions of each other. In case G ≆ H , G and H are said to be non-reconstructible . We describe the construction of a family of non-reconstructible 3-hypergraphs with 2 n +2 m vertices, for all n, m ⩾1.