Abstract
We investigate the H-property for step-graphons. Specifically, we sample graphs Gn on n nodes from a step-graphon and evaluate the probability that Gn has a Hamiltonian decomposition in the asymptotic regime as n → ∞. It has been shown in Belabbas and Chen (2023); Belabbas et al. (2021) 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.
Committee Chair
Xudong Chen
Committee Members
Hong Hu Netanel Raviv
Degree
Master of Science (MS)
Author's Department
Electrical & Systems Engineering
Document Type
Thesis
Date of Award
Spring 5-12-2025
Language
English (en)
DOI
https://doi.org/10.7936/2yzc-xa75
Recommended Citation
Gao, Wanting, "On the H-property for Step-graphons: Residual Case" (2025). McKelvey School of Engineering Theses & Dissertations. 1205.
The definitive version is available at https://doi.org/10.7936/2yzc-xa75
Included in
Control Theory Commons, Probability Commons, Systems Science Commons