Convergent Sequences of Dense Graphs II . Multiway Cuts and Statistical Physics

@inproceedings{Borgs2007ConvergentSO,
title={Convergent Sequences of Dense Graphs II . Multiway Cuts and Statistical Physics},
author={Christian Borgs and Jennifer T. Chayes and L{\'a}szl{\'o} Lov{\'a}sz and Vera T. S{\'o}s and Katalin Vesztergombi},
year={2007}
}

We consider sequences of graphs (Gn) and define various notions of convergence related to these sequences including “left convergence,” defined in terms of the densities of homomorphisms from small graphs into Gn, and “right convergence,” defined in terms of the densities of homomorphisms from Gn into small graphs. We show that right convergence is equivalent to left convergence, both for simple graphs Gn, and for graphs Gn with nontrivial nodeweights and edgeweights. Other equivalent… CONTINUE READING