Graphon与$H$-性质
Graphons and the $H$-property
AI总结：
本文研究graphon的$H$-性质，即从中采样的图几乎必然包含哈密顿分解，提出了保证一般无限维graphon满足该性质的条件，从而克服了有限维step-graphon结果无法直接推广的困难。
摘要：
如果一个graphon满足$H$-性质，则从中采样的图几乎必然包含哈密顿分解，这进而意味着相应的网络拓扑结构是结构稳定且结构集合可控的。在近期论文中，我们提出了一组条件，该条件对于有限维step-graphon类满足$H$-性质是本质上必要的且充分的。由于上述条件依赖于无法直接推广至无限维情形的对象，向一般graphon的无限维情形推广受到了阻碍。我们在此概述了绕过该困难的方法，并给出了保证一般graphon满足$H$-性质的条件。
英文摘要：
A graphon satisfies the $H$-property if graphs sampled from it contain a Hamiltonian decomposition almost surely, which in turn implies that the corresponding network topologies are, e.g., structurally stable and structurally ensemble controllable. In recent papers, we have exhibited a set of conditions that is essentially necessary and sufficient for the $H$-property to hold for the finite-dimensional class of step-graphons. The extension to the infinite-dimensional case of general graphons was hindered by the fact that said conditions relied on objects that do not admit immediate extensions to the infinite-dimensional case. We outline here our approach to bypass this difficulty and state conditions that guarantee that the $H$-property holds for general graphons.
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。
