Informace o publikaci

Compactness and finite forcibility of graphons

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GLEBOV Roman KRÁĽ Daniel VOLEC Jan

Rok publikování 2019
Druh Článek v odborném periodiku
Časopis / Zdroj Journal of the European Mathematical Society
Fakulta / Pracoviště MU

Fakulta informatiky

Citace
www http://dx.doi.org/10.4171/JEMS/901
Doi http://dx.doi.org/10.4171/JEMS/901
Klíčová slova Graph limits; extremal combinatorics
Popis 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.