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A smoother notion of spread hypergraphs

Part of: Graph theory

Published online by Cambridge University Press:  08 June 2023

Sam Spiro
Sam Spiro*
Affiliation:
Department of Mathematics, University of California San Diego, La Jolla, CA, USA
*
E-mail: sspiro@ucsd.edu
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Abstract

Alweiss, Lovett, Wu, and Zhang introduced $q$-spread hypergraphs in their breakthrough work regarding the sunflower conjecture, and since then $q$-spread hypergraphs have been used to give short proofs of several outstanding problems in probabilistic combinatorics. A variant of $q$-spread hypergraphs was implicitly used by Kahn, Narayanan, and Park to determine the threshold for when a square of a Hamiltonian cycle appears in the random graph $G_{n,p}$. In this paper, we give a common generalization of the original notion of $q$-spread hypergraphs and the variant used by Kahn, Narayanan, and Park.

Keywords

thresholdshypergraphsspread

MSC classification

Primary: 05C80: Random graphs
Type
Paper
Information
Combinatorics, Probability and Computing , Volume 32 , Issue 5 , September 2023 , pp. 809 - 818
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Copyright
© The Author(s), 2023. Published by Cambridge University Press

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Footnotes

This material is based upon work supported by the National Science Foundation Graduate Research Fellowship under Grant No. DGE-1650112.

References

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