A new generalization of Mantelʹs theorem to k-graphs

Let the k-graph Fan k consist of k edges that pairwise intersect exactly in one vertex x, plus one more edge intersecting each of these edges in a vertex different from x. We prove that, for n sufficiently large, the maximum number of edges in an n-vertex k-graph containing no copy of Fan k is ∏ i = 1 k ⌊ n + i − 1 k ⌋ , which equals the number of edges in a complete k-partite k-graph with almost equal parts. This is the only extremal example. This result is a special case of our more general theorem that applies to a larger class of excluded configurations.