Publication details

Compactness and finite forcibility of graphons

Authors

GLEBOV Roman KRÁĽ Daniel VOLEC Jan

Year of publication 2019
Type Article in Periodical
Magazine / Source Journal of the European Mathematical Society
MU Faculty or unit

Faculty of Informatics

Citation
Web http://dx.doi.org/10.4171/JEMS/901
Doi http://dx.doi.org/10.4171/JEMS/901
Keywords Graph limits; extremal combinatorics
Description Graphons are analytic objects associated with convergent sequences of graphs. Problems from extremal combinatorics and theoretical computer science led to a study of graphons determined by finitely many subgraph densities, which are referred to as finitely forcible. Following the intuition that such graphons should have finitary structure, Lovasz and Szegedy conjectured that the topological space of typical vertices of a finitely forcible graphon is always compact. We disprove the conjecture by constructing a finitely forcible graphon such that the associated space is not compact. The construction method gives a general framework for constructing finitely forcible graphons with non-trivial properties.