Bounding the number of hyperedges in friendship r-hypergraphs

@article{Gunderson2016BoundingTN,
  title={Bounding the number of hyperedges in friendship r-hypergraphs},
  author={Karen Gunderson and Natasha Morrison and Jason Semeraro},
  journal={Eur. J. Comb.},
  year={2016},
  volume={51},
  pages={125-134}
}
1 Citations
Symmetry in Domination for Hypergraphs with Choice
TLDR
The concept of (pair-wise) domination graphs for hypergraphs endowed with a choice function on edges is introduced and theorems regarding the existence of balanced (zero-edge) dominationGraphs are presented.

References

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TLDR
This note shows that if (X,B) is a friendship 3-hypergraph with |X| = n, then |B| ≥ d2(n − 1)(n − 2)/3e, and shows that this bound is met if and only if (Z,B), the set of 3-subsets of X, is a universal friend 3- hypergraph.
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A 3‐uniform friendship hypergraph is a 3‐uniform hypergraph in which, for all triples of vertices x, y, z there exists a unique vertex w, such that xyw , xzw, and yzw are edges in the hypergraph. Sós
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The well‐known Friendship Theorem states that if G is a graph in which every pair of vertices has exactly one common neighbor, then G has a single vertex joined to all others (a “universal friend”).
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