具有几乎任意结构的强有力的graphons
Finitely forcible graphons with an almost arbitrary structure
摘要：
图子是表示大型图的收敛序列的分析对象。如果一个图子是由许多子图密度决定的，即，如果由这样的图子表示的图的渐近结构仅依赖于1000个密度约束。这样的图子出现在各种场景中，特别是在极值组合学中。Lovasz和Szegedy指出，所有非强制图子都具有简单的结构。库珀、克拉尔和马丁斯在很强的意义上反驳了这一点，他们证明了任何图子都是一个可迫图子的子图子。我们通过证明对于每个$\varepsilon>0$，任何图子都跨越一个可强制图子的$1-\varepsilon$比例来加强这个结果。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
