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