# Paths, cycles and sprinkling in random hypergraphs

@inproceedings{Cooley2021PathsCA, title={Paths, cycles and sprinkling in random hypergraphs}, author={Oliver Cooley}, year={2021} }

We prove a lower bound on the length of the longest j-tight cycle in a k-uniform binomial random hypergraph for any 2 ≤ j ≤ 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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