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A k-graph, H = (V,E), is tight if for every surjective mapping f : V + { 1,. . . , k } there exists an edge a E f such that f l , is injective. Clearly, 2-graphs are tight if and only if they are connected. Bounds for the minimum number p," of edges in a tight k-graph with n vertices are given. We conjecture that p : = [n(n -2)/31 for every n and prove the equality when 2n + 1 is prime. From the examples, minimal embeddings of complete graphs into surfaces follow.

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