The Asymptotic Distributions of 3-star factors in random d-regular graphs
Lyra Yulianti

TL;DR
This paper applies the Small Subgraph Conditioning Method to determine the asymptotic distribution of 3-star factors in random d-regular graphs for d ≥ 4, extending understanding of subgraph distributions in such graphs.
Contribution
It introduces the use of the Small Subgraph Conditioning Method to analyze the distribution of 3-star factors in random d-regular graphs, a novel application for this specific subgraph type.
Findings
Asymptotic distribution of 3-star factors determined for d ≥ 4
Method extends analysis of regular subgraphs in random graphs
Provides probabilistic insights into subgraph counts in d-regular graphs
Abstract
The Small Subgraph Conditioning Method has been used to study the almost sure existence and the asymptotic distribution of the number of regular spanning subgraphs of various types in random \emph{d}-regular graphs. In this paper we use the method to determine the asymptotic distribution of the number of 3-star factors in random \emph{d}-regular graphs for
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Taxonomy
TopicsLimits and Structures in Graph Theory · Advanced Graph Theory Research · Graph theory and applications
