Our main results are quantitative bounds in the multivariate normal approximation of centred subgraph counts random graphs generated by a general graphon and independent vertex labels. We interested these statistics because they key to understanding fluctuations regular — cornerstone dense graph limit theory. also identify resulting limiting Gaussian stochastic measures means theory generalised...

The semi-random graph process is a single player game in which the initially presented an empty on n vertices. In each round, vertex u to independently and uniformly at random. then adaptively selects v, adds edge uv graph. For fixed monotone property, objective of force satisfy this property with high probability as few rounds possible. We focus problem constructing Hamilton cycle particular, ...

We introduce a process where connected rooted multigraph evolves by splitting events on its vertices, occurring randomly in continuous time. When vertex splits, incoming edges are assigned between offspring and Poisson random number of added them. The is parametrised positive real λ which governs the limiting average degree. show that for each value there unique M(λ) invariant under this evolut...