Date of Award

Winter 1-2017

Embargo Period

7-6-2017

Degree Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Mathematical Sciences

Advisor(s)

Alan Frieze

Abstract

This thesis is concerned with the study of random graphs and random algorithms. There are three overarching themes. One theme is sparse random graphs, i.e. random graphs in which the average degree is bounded with high probability. A second theme is that of finding spanning subsets such as spanning trees, perfect matchings and Hamilton cycles. A third theme is solving optimization problems on graphs with random edge costs.

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