A greedy algorithm for finding a large 2‐matching on a random cubic graph

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 − κ(U ) where n is the number of vertices of G and κ denotes the number of components. In this paper, 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 κ(U ) =Θ n 1/5 .

An improved lower bound on the length of the longest cycle in random graphs

“…The specific version of the 2-Greedy algorithm is taken from [4] while variations and extensions of it have also been studied in [3], [5] and [17]. The 2-Greedy algorithm sequentially grows a 2-matching M .…”