Year: 2025
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Authors: Gao, Wanting, Chen, Xudong
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: National Science Foundation
OpenAlex ID: W4407832014