منابع مشابه
On the VC-dimension of uniform hypergraphs
Let F be a k-uniform hypergraph on [n] where k − 1 is a power of some prime p and n ≥ n0(k). Our main result says that if |F | > ( n k−1 ) − logp n + k!kk , then there exists E0 ∈ F such that {E ∩ E0 : E ∈ F} contains all subsets of E0. This improves a longstanding bound of ( n k−1 ) due to Frankl and Pach [7].
متن کاملDomination game on uniform hypergraphs
In this paper we introduce and study the domination game on hypergraphs. This is played on a hypergraph H by two players, namely Dominator and Staller, who alternately select vertices such that each selected vertex enlarges the set of vertices dominated so far. The game is over if all vertices of H are dominated. Dominator aims to finish the game as soon as possible, while Staller aims to delay...
متن کاملSpectra of Uniform Hypergraphs
We present a spectral theory of uniform hypergraphs that closely parallels Spectral Graph Theory. A number of recent developments building upon classical work has led to a rich understanding of “symmetric hyperdeterminants” of hypermatrices, a.k.a. multidimensional arrays. Symmetric hyperdeterminants share many properties with determinants, but the context of multilinear algebra is substantiall...
متن کاملOn 3-uniform hypergraphs without linear cycles∗
We explore properties of 3-uniform hypergraphs H without linear cycles. It is surprising that even the simplest facts about ensuring cycles in graphs can be fairly complicated to prove for hypergraphs. Our main results are that 3-uniform hypergraphs without linear cycles must contain a vertex of strong degree at most two and must have independent sets of size at least 2|V (H)| 5 .
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 ...
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ژورنال
عنوان ژورنال: European Journal of Combinatorics
سال: 2018
ISSN: 0195-6698
DOI: 10.1016/j.ejc.2018.02.034