Informace o publikaci

Infinite-dimensional finitely forcible graphon

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GLEBOV Roman KLIMOŠOVÁ Tereza KRÁĽ Daniel

Rok publikování 2019
Druh Článek v odborném periodiku
Časopis / Zdroj Proceedings of the London mathematical society
Fakulta / Pracoviště MU

Fakulta informatiky

Citace
www http://dx.doi.org/10.1112/plms.12203
Doi http://dx.doi.org/10.1112/plms.12203
Klíčová slova Graph limits; large graphs
Popis Graphons are analytic objects associated with convergent sequences of dense graphs. Finitely forcible graphons, that is, those determined by finitely many subgraph densities, are of particular interest because of their relation to various problems in extremal combinatorics and theoretical computer science. Lovasz and Szegedy conjectured that the topological space of typical vertices of a finitely forcible graphon always has finite dimension, which would have implications on the minimum number of parts in its weak epsilon-regular partition. We disprove the conjecture by constructing a finitely forcible graphon with the space of typical vertices that has infinite dimension.