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 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 .