A new generalization of Mantel's theorem to k-graphs

@article{Mubayi2007ANG,
  title={A new generalization of Mantel's theorem to k-graphs},
  author={Dhruv Mubayi and Oleg Pikhurko},
  journal={J. Comb. Theory, Ser. B},
  year={2007},
  volume={97},
  pages={669-678}
}
Let the k-graph Fan 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 is ∏ k 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… CONTINUE READING

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