Date of Award

2013

Degree Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Graduate Group

Mathematics

First Advisor

Robin Pemantle

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.

Included in

Mathematics Commons

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