On the minimum size of tight hypergraphs

A k-graph, H = (V, E), is tight if for every surjective mapping f: V {1,….k} there exists an edge α ϵ E sicj tjat f|α is injective. Clearly, 2-graphs are tight if and only if they are connected. Bounds for the minimum number ϕ of edges in a tight k-graph with n vertices are given. We conjecture that ϕ for every n and prove the equality when 2n + 1 is prime. From the examples, minimal embeddings of complete graphs into surfaces follow. © 1992 John Wiley & Sons, Inc.