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arXiv · 1809.05973

Finitely forcible graphons with an almost arbitrary structure

Daniel Kral·László Miklós Lovász·Jonathan A. Noel·Jakub Sosnovec
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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 $\varepsilon>0$ that any graphon spans a $1-\varepsilon$ proportion of a finitely forcible graphon.

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Daniel Kral, László Miklós Lovász, Jonathan A. Noel, Jakub Sosnovec. 2018-09-16. Finitely forcible graphons with an almost arbitrary structure. https://arxiv.org/abs/1809.05973

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