arXiv subjects

Wanting Gao

Publications and source records attributed to Wanting Gao.

2 recordsLinked to original sources

arXiv2026

Convergence rate of $H$-property for step-graphons

A graphon is said to have the $H$-property if a random undirected graph $G_n$ on $n$ nodes sampled from it has a node-wise disjoint cycle cover almost surely as $n\to\infty$. It has been shown in the earlier work that the $H$-property obeys the zero-one law, i.e., the probability that the random graph has a cycle cover tends to either one or zero. In this paper, we sharpen the result by characterizing the convergence rate of the probability. Specifically, we show that there are two different types of rates, with one being exponential and the other being root $n$. We provide a rigorous proof and numerical validation.

math.PR↗

arXiv2025

On the $H$-property for Step-graphons: The Residual Case

We investigate the $H$-property for step-graphons. Specifically, we sample graphs $G_n$ on $n$ nodes from a step-graphon and evaluate the probability that $G_n$ has a Hamiltonian decomposition in the asymptotic regime as $n\to\infty$. It has been shown that for almost all step-graphons, this probability converges to either zero or one. We focus in this paper on the residual case where the zero-one law does not apply. We show that the limit of the probability still exists and provide an explicit expression of it. We present a complete proof of the result and validate it through numerical studies.

eess.SY↗