Breadcrumb
Randomised reproducing graphs
Thu 17 January 2013, 16:30
Jonathan Jordan
Sheffield
Organisers: Tom McCourt, Tony Nixon, Karen Gunderson
ABSTRACT
We introduce a model for a growing random graph based on simultaneous
reproduction of the vertices. The model can be thought of as a generalisation of the reproducing graphs of Southwell and Cannings and Bonato et al to allow for a random element, and there are three parameters, $\alpha$, $\beta$ and $\gamma$, which are the probabilities of edges appearing between different types of vertices. We show that as the probabilities associated with the model vary there are a number of phase transitions, in particular concerning the degree sequence. We also give some results on the number of edges and on the spectral gap.