The 2-core of a random inhomogeneous hypergraph / Omar Abuzzahab.
vii, 88 p. ; 29 cm.
- Local subjects:
- Penn dissertations -- Mathematics.
Mathematics -- Penn dissertations.
- 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.
- Adviser: Robin Pemantle.
Thesis (Ph.D. in Mathematics) -- University of Pennsylvania, 2013.
Includes bibliographical references.
- Pemantle, Robin, advisor.
Steele, Michael committee member.
Kannan, Sampath committee member.
Scedrov, Andre committee member.
University of Pennsylvania. Mathematics.
|Location||Notes||Your Loan Policy|
|Description||Status||Barcode||Your Loan Policy|