A Doubling Construction for 3-Uniform Friendship Hypergraphs with the Universal Pairs Property
نویسندگان
چکیده
منابع مشابه
On 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, ...
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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...
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For a Boolean function f, let D(f) denote its deterministic decision tree complexity, i.e., minimum number of (adaptive) queries required in worst case in order to determine f. In a classic paper, Rivest and Vuillemin [19] show that any non-constant monotone property P : {0, 1}( n 2) → {0, 1} of n-vertex graphs has D(P) = Ω(n). We extend their result to 3-uniform hypergraphs. In particular, we ...
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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 ...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Designs
سال: 2015
ISSN: 1063-8539
DOI: 10.1002/jcd.21509