The size of the giant component in random hypergraphs: a short proof

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• Christoph Koch (University of Oxford)
• Tuesday 13 March 2018, 15:00-16:00
• Watson LTA.

If you have a question about this talk, please contact Allan Lo.

We consider connected components in k-uniform hypergraphs for the following notion of connectedness: given integers k> 1 and 0< j < k, two j-sets (j-tuples of distinct vertices) lie in the same j-component if there is a sequence of edges from one to the other such that consecutive edges intersect in at least j vertices.

We prove that certain collections of j-sets constructed during a breadth-first search process on j-components in a random k-uniform hypergraph are reasonably regularly distributed with high probability. As an application we provide a short proof of the asymptotic size of the giant j-component shortly after it appears.

This is joint work with Oliver Cooley and Mihyun Kang.

This talk is part of the Combinatorics and Probability Seminar series.

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• Combinatorics and Probability Seminar
• School of Mathematics Events
• Watson LTA

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