The 2-Core of a Random Inhomogeneous Hypergraph

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Doctor of Philosophy (PhD)
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Mathematics
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Mathematics
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2014-08-20T00:00:00-07:00
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Abstract

The k-core of a hypergraph is the unique subgraph where all vertices have degree at least k and which is the maximal induced subgraph with this property. We study the 2-core of a random hypergraph by probabilistic analysis of the following edge removal rule: remove any vertices with degree less than 2, and remove all hyperedges incident to these vertices. This process terminates with the 2-core. The hypergraph model studied is an inhomogeneous model --- where the expected degrees are not identical. The main result we prove is that as the number of vertices n tends to infinity, the number of hyperedges R in the 2-core obeys a limit law: R/n converges in probability to a non-random constant.

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Robin Pemantle
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2013-01-01
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