Degree Sequences of Random Bipartite Graphs

This concerns three random bipartite graph models. For each random graph model a binomially based model is explicitly constructed which has the property that for ‘most’ degree sequences (s, t), the probability of (s, t) in the graph model is asymptotically approximated by the probability of (s, t) in the binomial model. This allows us to prove Theorems 7.4 and 7.5 which are the bipartite analogue of Theorem 2.6 in the paper by McKay and Wormald [MW97]. This construction is new as are Theorems 7.4 and 7.5. Acknowledgements It is an honor for me to thank both my co-supervisors Prof. Brendan Mckay and Dr. Judy-anne Osborn. I would like to thank Brendan Mckay for his unending fountain of mathematical insight and interesting ideas. I would also like to show my gratitude to Judy-anne Osborn for her time and help in writing the thesis. Their patience and under-standing made this thesis possible. I am also indebted to Dr. Adam Rennie for his advice on the art of mathematical writing and thank him for his help. Also to my fellow honours students, especially Brendan Fong