Bounding the number of hyperedges in friendship r-hypergraphs

  title={Bounding the number of hyperedges in friendship r-hypergraphs},
  author={Karen Gunderson and Natasha Morrison and Jason Semeraro},
  journal={Eur. J. Comb.},
For r ? 2 , an r -uniform hypergraph is called a friendship r -hypergraph if every set R of r vertices has a unique 'friend' - that is, there exists a unique vertex x ? R with the property that for each subset A ? R of size r - 1 , the set A ? { x } is a hyperedge.We show that for r ? 3 , the number of hyperedges in a friendship r -hypergraph is at least r + 1 r ( n - 1 r - 1 ) , and we characterise those hypergraphs which achieve this bound. This generalises a result given by Li and van Rees… 
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