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Forbidding Complete Hypergraphs as Traces.

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Title: Forbidding Complete Hypergraphs as Traces.
Authors: Mubayi, Dhruv1 mubayi@math.uic.edu, Yi Zhao2 yizhao@mathstat.gsu.edu
Source: Graphs & Combinatorics. Dec2007, Vol. 23 Issue 6, p667-679. 13p.
Subjects: Hypergraphs, Fuzzy hypergraphs, Matrices (Mathematics), Combinatorics, Graphic methods, Graph theory
Abstract: Let 2 ≤ q ≤min{ p, t − 1} be fixed and n → ∞. Suppose that $$\mathcal{F}$$ 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 $${\mathcal{F}}$$ in many cases. For example, when q = 2 and p∈{ t, t + 1}, the maximum is $$( \frac{n}{t-1})^{t-1} + o(n^{t-1})$$ , and when p = t = 3, it is $$\lfloor \frac{(n-1)^2}{4}\rfloor$$ for all n≥ 3. Our proofs use the Kruskal-Katona theorem, an extension of the sunflower lemma due to Füredi, and recent results on hypergraph Turán numbers. [ABSTRACT FROM AUTHOR]
Copyright of Graphs & Combinatorics is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: <searchLink fieldCode="JN" term="%22Graphs+%26+Combinatorics%22">Graphs & Combinatorics</searchLink>. Dec2007, Vol. 23 Issue 6, p667-679. 13p.
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  Data: <searchLink fieldCode="DE" term="%22Hypergraphs%22">Hypergraphs</searchLink><br /><searchLink fieldCode="DE" term="%22Fuzzy+hypergraphs%22">Fuzzy hypergraphs</searchLink><br /><searchLink fieldCode="DE" term="%22Matrices+%28Mathematics%29%22">Matrices (Mathematics)</searchLink><br /><searchLink fieldCode="DE" term="%22Combinatorics%22">Combinatorics</searchLink><br /><searchLink fieldCode="DE" term="%22Graphic+methods%22">Graphic methods</searchLink><br /><searchLink fieldCode="DE" term="%22Graph+theory%22">Graph theory</searchLink>
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  Data: Let 2 ≤ q ≤min{ p, t − 1} be fixed and n → ∞. Suppose that $$\mathcal{F}$$ 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 $${\mathcal{F}}$$ in many cases. For example, when q = 2 and p∈{ t, t + 1}, the maximum is $$( \frac{n}{t-1})^{t-1} + o(n^{t-1})$$ , and when p = t = 3, it is $$\lfloor \frac{(n-1)^2}{4}\rfloor$$ for all n≥ 3. Our proofs use the Kruskal-Katona theorem, an extension of the sunflower lemma due to Füredi, and recent results on hypergraph Turán numbers. [ABSTRACT FROM AUTHOR]
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  Data: <i>Copyright of Graphs & Combinatorics is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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      – SubjectFull: Matrices (Mathematics)
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              Text: Dec2007
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