Hamiltonicity of Step-graphon

Xudong Chen

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arXiv · 2510.02074

Hamiltonicity of Step-graphon

Xudong Chen

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Abstract

A step-graphon has the strong (resp., weak) $H$-property if a directed, random graph sampled from it has a Hamilton cycle (resp., a node-wise disjoint cycle cover) asymptotically almost surely. The weak/strong $H$-property is essentially a zero-one property. We identify key objects associated with the step-graphon that matter for the zero-one law and provide a complete characterization.

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Xudong Chen. 2025-10-02. Hamiltonicity of Step-graphon. https://arxiv.org/abs/2510.02074

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