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 $n-\k(U)$ where
n
is the number of vertices of
G
and $\k$ denotes the number of components. In this paper, we analyze the performance of a greedy algorithm \textsc{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 $\k(U) = \tilde{\Theta}\of{n^{1/5}}$.