Abstract
AbstractAlweiss, 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.
Publisher
Cambridge University Press (CUP)
Subject
Applied Mathematics,Computational Theory and Mathematics,Statistics and Probability,Theoretical Computer Science
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