Date of Award
Spring 5-12-2025
Degree Name
Master of Science (MS)
Degree Type
Thesis
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.
Language
English (en)
Chair
Xudong Chen
Committee Members
Hong Hu Netanel Raviv
Included in
Control Theory Commons, Probability Commons, Systems Science Commons