منابع مشابه
Friendship 3-hypergraphs
A friendship 3-hypergraph is a 3-hypergraph in which any 3 vertices, u, v and w, occur in pairs with a unique fourth vertex x; i.e., uvx, uwx, vwx are 3-hyperedges. S os found friendship 3-hypergraphs coming from Steiner Triple Systems. Hartke and Vandenbussche showed that any friendship 3-hypergraph can be decomposed into sets of K 4 's. We think of this as a set of 4-tuples and call it a frie...
متن کاملOn a Question of Sós About 3-Uniform Friendship Hypergraphs
The well-known Friendship Theorem states that ifG 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”). V. Sós defined an analogous friendship property for 3-uniformhypergraphs, andgave a construction satisfying the friendshipproperty that has auniversal friend.Wepresent new 3-uniformhypergraphs on 8, ...
متن کاملBounding the Number of Hyperedges in Friendship $r$-Hypergraphs
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...
متن کاملPartitioning 3-uniform hypergraphs
Bollobás and Thomason conjectured that the vertices of any r-uniform hypergraph with m edges can be partitioned into r sets so that each set meets at least rm/(2r − 1) edges. For r = 3, Bollobás, Reed and Thomason proved the lower bound (1− 1/e)m/3 ≈ 0.21m, which was improved to 5m/9 by Bollobás and Scott (while the conjectured bound is 3m/5). In this paper, we show that this Bollobás-Thomason ...
متن کاملMatchings in 3-uniform hypergraphs
We determine the minimum vertex degree that ensures a perfect matching in a 3-uniform hypergraph. More precisely, suppose thatH is a sufficiently large 3-uniform hypergraph whose order n is divisible by 3. If the minimum vertex degree of H is greater than ( n−1 2 )
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2012
ISSN: 0012-365X
DOI: 10.1016/j.disc.2012.02.025