•
Publication Date: 2006
Publication Name: Proceedings of the thirty-eighth annual ACM symposium on Theory of computing - STOC '06
Research Interests:
•
Publication Date: 2006
Publication Name: Algorithms and Combinatorics
Research Interests:
•
by Christian Borgs and Vera Sós
Publication Date: 2012
Publication Name: Annals of Mathematics
Research Interests:
•
by Christian Borgs and Vera Sós
Publication Date: 2008
Publication Name: Advances in Mathematics
Research Interests:
•
Motivated in part by various sequences of graphs growing under random rules (like internet models), convergent sequences of dense graphs and their limits were introduced by Borgs, Chayes, Lov\'asz, S\'os and Vesztergombi and by Lov\'asz... more
Motivated in part by various sequences of graphs growing under random rules (like internet models), convergent sequences of dense graphs and their limits were introduced by Borgs, Chayes, Lov\'asz, S\'os and Vesztergombi and by Lov\'asz and Szegedy. In this paper we use this framework to study one of the motivating class of examples, namely randomly growing graphs. We prove the (almost sure) convergence of several such randomly growing graph sequences, and determine their limit. The analysis is not always straightforward: in some cases the cut distance from a limit object can be directly estimated, in other case densities of subgraphs can be shown to converge.