Spanning Structures of Graphs

This PhD thesis is formed of work completed while studying at Royal Holloway, University of London. The three chapters that form the majority of the thesis each represent distinct projects that were studied in this time.
Chronologically, the research forming the first chapter, on factors in random graphs was the first to be completed, in collaboration with my supervisor, Stefanie Gerke. This culminated in the paper ‘Non-vertex balanced factors in random graphs’, published by the Journal of Graph Theory in 2014 [30].
The second chapter, titled Complexity on Eulerian circuits, was work done in collaboration with Iain Moffatt of Royal Holloway and Joanna A. Ellis-Monaghan and Greta Pangborn of Saint Michael’s College, Colchester in the US. This work is largely encapsulated by the paper ‘DNA origami and the complexity of Eulerian circuits with turning costs’ published by the journal Natural Computing in 2014 [17].
The third chapter, on Adversarial resilience of matchings was work carried out in collaboration with Stefanie Gerke and Paul Balister of the University of Memphis. We aim to publish the results of this chapter in the near future.