Traces of hypergraphs
نویسندگان
چکیده
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...
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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...
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for a given hypergraph $h$ with chromatic number $chi(h)$ and with no edge containing only one vertex, it is shown that the minimum number $l$ for which there exists a partition (also a covering) ${e_1,e_2,ldots,e_l}$ for $e(h)$, such that the hypergraph induced by $e_i$ for each $1leq ileq l$ is $k$-colorable, is $lceil log_{k} chi(h) rceil$.
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ژورنال
عنوان ژورنال: Journal of the London Mathematical Society
سال: 2019
ISSN: 0024-6107,1469-7750
DOI: 10.1112/jlms.12233