Finitely forcible graphons with an almost arbitrary structure
Combinatorics
2020-07-29 v2
Abstract
Graphons are analytic objects representing convergent sequences of large graphs. A graphon is said to be finitely forcible if it is determined by finitely many subgraph densities, i.e., if the asymptotic structure of graphs represented by such a graphon depends only on finitely many density constraints. Such graphons appear in various scenarios, particularly in extremal combinatorics. Lovasz and Szegedy conjectured that all finitely forcible graphons possess a simple structure. This was disproved in a strong sense by Cooper, Kral and Martins, who showed that any graphon is a subgraphon of a finitely forcible graphon. We strenghten this result by showing for every that any graphon spans a proportion of a finitely forcible graphon.
Keywords
Cite
@article{arxiv.1809.05973,
title = {Finitely forcible graphons with an almost arbitrary structure},
author = {Daniel Kral and László Miklós Lovász and Jonathan A. Noel and Jakub Sosnovec},
journal= {arXiv preprint arXiv:1809.05973},
year = {2020}
}