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   n kof edges in a tight k ‐graph with n vertices are given. We conjecture that ϕ   n 3for every n and prove the equality when 2 n + 1 is prime. From the examples, minimal embeddings of complete graphs into surfaces follow. © 1992 John Wiley & Sons, Inc.