Publication at Faculty of Mathematics and Physics |
2011
Abstract
Is there a notion of limit for growing graph sequences? What kind of object is this limit? Which graph parameters behave "continuously" when passing to the limit? Limits of graph sequences can be defined in more than one setting. The case when the graphs in question are dense is best understood.
In this case, convergence and limits were defined by Borgs, Chayes, Lovász, Sós, Szegedy and Vesztergombi (2006), and the ensuing theory shed new light on graph homomorphisms, Szemerédi''s regularity lemma, quasi-random graphs, graph testing and extremal graph theory.