#### Document Type

Article

#### Publication Date

7-1-2018

#### Journal / Book Title

Journal of Graph Theory

#### Abstract

A 2-matching of a graph G is a spanning subgraph with maximum degree two. The size of a 2-matching U is the number of edges in U and this is at least n-k(U) where n is the number of vertices of G and κ denotes the number of components. In this article, we analyze the performance of a greedy algorithm 2greedy for finding a large 2-matching on a random 3-regular graph. We prove that with high probability, the algorithm outputs a 2-matching U with k(U)=Θ(n1/5).

#### DOI

10.1002/jgt.22224

#### MSU Digital Commons Citation

Bal, Deepak; Bennett, Patrick; Bohman, Tom; and Frieze, Alan, "A Greedy Algorithm for Finding a Large 2-Matching on a Random Cubic Graph" (2018). *Department of Mathematics Facuty Scholarship and Creative Works*. 32.

https://digitalcommons.montclair.edu/mathsci-facpubs/32

#### Published Citation

Bal, D., Bennett, P., Bohman, T., & Frieze, A. (2018). A greedy algorithm for finding a large 2‐matching on a random cubic graph. Journal of Graph Theory, 88(3), 449-481.