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

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 $d \geq 4$