jbriggs_mathsci_2018.pdf (1.01 MB)
Online Algorithms and Extremal Structures
We study several problems in probabilistic and extremal combinatorics. Probabilistic combinatorics is the area of mathematics studying the behaviour of \most" discrete structures in a given family, as opposed to extremal combinatorics, where one is concerned with the behaviour of \the best" structure with respect to a discrete parameter.
The largest branch of probabilistic combinatorics is the field of random graphs. Given a probability distribution on a collection of graphs, we wish to determine whether a graphtheoretic property is likely to arise or not.
The largest branch of probabilistic combinatorics is the field of random graphs. Given a probability distribution on a collection of graphs, we wish to determine whether a graphtheoretic property is likely to arise or not.
History
Date
2018-08-01Degree Type
- Dissertation
Department
- Mathematical Sciences
Degree Name
- Doctor of Philosophy (PhD)