A Greedy Algorithm for Finding a Large 2-Matching on a Random Cubic Graph

Authors

• Deepak Bal, Montclair State UniversityFollow
• Patrick Bennett, Carnegie Mellon University
• Tom Bohman, Carnegie Mellon University
• Alan Frieze, Tel Aviv University

Document Type

Preprint

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