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oaioai:digitalcommons.memphis.edu:facpubs-5485

Daisies and other Turán problems

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Publication date
1 September 2011
Publisher
University of Memphis Digital Commons
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    Abstract

    Daisy, a hypergraph and other Turán problems in the hypercube are studied. A daisy, or r-daisy, is a certain r-uniform hypergraph consisting of six sets. Given an (r - 2)-set P and a 4-set Q disjoint from P, the daisy on (P,Q) consists of the r-sets A with P ⊂ A ⊂ P ∪ Q. A beautiful conjecture of Johnson and Talbot is proposed, about meeting d-cubes in several points, that is also closely tied to daisy problems. They conjecture that if there is a positive fraction of the vertices of the n-cube then (for n sufficiently large) there must be some d-cube containing the least points of the family

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    Last time updated on 05/05/2022

    This paper was published in University of Memphis Digital Commons.

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