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Paths, cycles and sprinkling in random hypergraphs

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 نشر من قبل Oliver Cooley
 تاريخ النشر 2021
  مجال البحث
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 تأليف Oliver Cooley




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We prove a lower bound on the length of the longest $j$-tight cycle in a $k$-uniform binomial random hypergraph for any $2 le j le k-1$. We first prove the existence of a $j$-tight path of the required length. The standard sprinkling argument is not enough to show that this path can be closed to a $j$-tight cycle -- we therefore show that the path has many extensions, which is sufficient to allow the sprinkling to close the cycle.



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