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arXiv · 2402.09692

Graphons and the $H$-property

Mohamed-Ali Belabbas·Xudong Chen
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Abstract

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.

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Mohamed-Ali Belabbas, Xudong Chen. 2024-02-15. Graphons and the $H$-property. https://arxiv.org/abs/2402.09692

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