On extremal problems concerning the traces of sets

Piga, Simón; Schülke, Bjarne

doi:10.1016/j.jcta.2021.105447

Journal of Combinatorial Theory, Series A

2021

DOI: 10.1016/j.jcta.2021.105447

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On extremal problems concerning the traces of sets

Simón Piga

Bjarne Schülke

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On Extremal Problems Concerning the Traces of Sets

Piga

Schülke

2021

Trends in Mathematics

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Let k ě 3. Given a k-uniform hypergraph H, the minimum codegree δpHq is the largest d P N such that every pk´1q-set of V pHq is contained in at least d edges. Given a k-uniform hypergraph F , the codegree Turán density γpF q of F is the smallest γ P r0, 1s such that every k-uniform hypergraph on n vertices with δpHq ě pγ `op1qqn contains a copy of F . Similarly as other variants of the hypergraph Turán problem, determining the codegree Turán density of a hypergraph is in general notoriously difficult and only few results are known.In this work, we show that for every ε ą 0, there is a k-uniform hypergraph F with 0 ă γpF q ă ε. This is in contrast to the classical Turán density, which cannot take any value in the interval p0, k!{k k q due to a fundamental result by Erdős.

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On Extremal Problems Concerning the Traces of Sets

Piga

Schülke

2021

Trends in Mathematics

Self Cite

View full text Add to dashboard Cite

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On extremal problems concerning the traces of sets

Cited by 1 publication

References 6 publications

On Extremal Problems Concerning the Traces of Sets

On Extremal Problems Concerning the Traces of Sets

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