منابع مشابه
Turán Problems on Non-Uniform Hypergraphs
A non-uniform hypergraph H = (V,E) consists of a vertex set V and an edge set E ⊆ 2V ; the edges in E are not required to all have the same cardinality. The set of all cardinalities of edges in H is denoted by R(H), the set of edge types. For a fixed hypergraph H, the Turán density π(H) is defined to be limn→∞maxGn hn(Gn), where the maximum is taken over all H-free hypergraphs Gn on n vertices ...
متن کاملNon-uniform Turán-type problems
Given positive integers n, k, t, with 2 ≤ k ≤ n, and t < 2, let m(n, k, t) be the minimum size of a family F of (nonempty distinct) subsets of [n] such that every k-subset of [n] contains at least t members of F , and every (k − 1)-subset of [n] contains at most t− 1 members of F . For fixed k and t, we determine the order of magnitude of m(n, k, t). We also consider related Turán numbers T≥r(n...
متن کاملCovering Non-uniform Hypergraphs
A subset of the vertices in a hypergraph is a cover if it intersects every edge. Let τ(H) denote the cardinality of a minimum cover in the hypergraph H , and let us denote by g(n) the maximum of τ(H) taken over all hypergraphs H with n vertices and with no two hyperedges of the same size. We show that g(n) < 1.98 √ n(1 + o(1)). A special case corresponds to an old problem of Erdős asking the ma...
متن کاملOn Ramsey - Turán type theorems for hypergraphs
Let H’ be an r-uniform hypergraph. Let g=g(n; F) be the minimal integer so that any r-uniform hypergraph on n vertices and more than g edges contains a subgraph isomorphic to H’. Let e=f(n; H’, en) denote the minimal integer such that every r-uniform hypergraph on n vertices with more than e edges and with no independent set of .sn vertices contains a subgraph isomorphic to H’. We show that if ...
متن کاملTurán numbers for Berge - hypergraphs and related 1 extremal problems
4 Let F be a graph. We say that a hypergraph H is a Berge-F if there is a bijection 5 f : E(F )→ E(H) such that e ⊆ f(e) for every e ∈ E(F ). Note that Berge-F actually 6 denotes a class of hypergraphs. The maximum number of edges in an n-vertex r-graph 7 with no subhypergraph isomorphic to any Berge-F is denoted exr(n,Berge-F ). In this 8 paper we establish new upper and lower bounds on exr(n,...
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2014
ISSN: 1077-8926
DOI: 10.37236/3901