Compactness and finite forcibility of graphons
Roman GlebovBen Gurion University of the Negev, Beer-Sheva, Israel
Daniel Král'Masaryk University, Brno, Czech Republic, and University of Warwick, Coventry, UK
Jan VolecEmory University, Atlanta, USA
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, Lovász 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.
Cite this article
Roman Glebov, Daniel Král', Jan Volec, Compactness and finite forcibility of graphons. J. Eur. Math. Soc. 21 (2019), no. 10, pp. 3199–3223DOI 10.4171/JEMS/901