منابع مشابه
Forbidding Complete Hypergraphs as Traces
Let 2 ≤ q ≤ min{p, t − 1} be fixed and n → ∞. Suppose that F is a p-uniform hypergraph on n vertices that contains no complete q-uniform hypergraph on t vertices as a trace. We determine the asymptotic maximum size of F in many cases. For example, when q = 2 and p ∈ {t, t+ 1}, the maximum is ( n t−1 ) t−1 + o(nt−1), and when p = t = 3, it is b (n−1) 2 4 c for all n ≥ 3. Our proofs use the Krusk...
متن کاملOn the Traces of Complete Hypergraphs
Let n ≥ t ≥ 3. Suppose that F is a family of t-element subsets of [n] satisfying |F| > ( n t−1 )t−1 + o(nt−1). Our main result implies that there exists a t-element subset S of [n] such that {E ∩ S : E ∈ F} contains all 2-element subsets of S, and this is asymptotically sharp. When t = 3, we prove the same result whenever |F| > ⌊ (n−1)2 4 ⌋ , which is sharp for all n ≥ 3. Our proofs use the Erd...
متن کاملForbidding Hamilton cycles in uniform hypergraphs
For 1 ≤ d ≤ ` < k, we give a new lower bound for the minimum d-degree threshold that guarantees a Hamilton `-cycle in k-uniform hypergraphs. When k ≥ 4 and d < ` = k − 1, this bound is larger than the conjectured minimum d-degree threshold for perfect matchings and thus disproves a wellknown conjecture of Rödl and Ruciński. Our (simple) construction generalizes a construction of Katona and Kier...
متن کاملCyclic partitions of complete nonuniform hypergraphs and complete multipartite hypergraphs
A cyclic q-partition of a hypergraph (V,E) is a partition of the edge set E of the form {F, F , F θ 2 , . . . , F θ q−1 } for some permutation θ of the vertex set V . Let Vn = {1, 2, . . . , n}. For a positive integer k, ( Vn k ) denotes the set of all k-subsets of Vn. For a nonempty subset K of Vn−1, we let K n denote the hypergraph ( Vn, ⋃ k∈K ( Vn k )) . In this paper, we find a necessary an...
متن کاملForbidding Kuratowski Graphs as Immersions
The immersion relation is a partial ordering relation on graphs that is weaker than the topological minor relation in the sense that if a graph G contains a graph H as a topological minor, then it also contains it as an immersion but not vice versa. Kuratowski graphs, namely K5 and K3,3, give a precise characterization of planar graphs when excluded as topological minors. In this note we give a...
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ژورنال
عنوان ژورنال: Graphs and Combinatorics
سال: 2007
ISSN: 0911-0119,1435-5914
DOI: 10.1007/s00373-007-0755-7