Finitely forcible graphons
Combinatorics
2013-08-23 v2
Abstract
We investigate families of graphs and graphons (graph limits) that are defined by a finite number of prescribed subgraph densities. Our main focus is the case when the family contains only one element, i.e., a unique structure is forced by finitely many subgraph densities. Generalizing results of Turan, Erdos-Simonovits and Chung-Graham-Wilson, we construct numerous finitely forcible graphons. Most of these fall into two categories: one type has an algebraic structure and the other type has an iterated (fractal-like) structure. We also give some necessary conditions for forcibility, which imply that finitely forcible graphons are "rare", and exhibit simple and explicit non-forcible graphons.
Cite
@article{arxiv.0901.0929,
title = {Finitely forcible graphons},
author = {Laszlo Lovasz and Balazs Szegedy},
journal= {arXiv preprint arXiv:0901.0929},
year = {2013}
}
Comments
revised version, 40 pages