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)
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