The 2-Core of a Random Inhomogeneous Hypergraph
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Degree type
Doctor of Philosophy (PhD)
Graduate group
Mathematics
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Subject
Mathematics
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Copyright date
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.
Advisor
Robin Pemantle
Date of degree
2013-01-01