Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6424040 | European Journal of Combinatorics | 2016 | 10 Pages |
Abstract
For râ¥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 xâR with the property that for each subset AâR of size râ1, the set Aâª{x} is a hyperedge.We show that for râ¥3, the number of hyperedges in a friendship r-hypergraph is at least r+1r(nâ1râ1), and we characterise those hypergraphs which achieve this bound. This generalises a result given by Li and van Rees in the case when r=3.We also obtain a new upper bound on the number of hyperedges in a friendship r-hypergraph, which improves on a known bound given by Li, van Rees, Seo and Singhi when r=3.
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Karen Gunderson, Natasha Morrison, Jason Semeraro,