1-restricted Simple 2-matchings: (Extended Abstract)

A simple 2-matching in a graph is a subgraph all of whose nodes have degree ≤ 2. A simple 2-matching is called k-restricted if every connected component has > k edges. We consider the problem of finding a k-restricted simple 2-matching with a maximum number of edges, which is a relaxation of the problem of finding a Hamilton cycle in a graph. Our main result is a new polynomial time algorithm for finding a 1-restricted simple 2-matching with a maximum number of edges. We also present a Tutte-type existence theorem and a Tutte-Berge-type formula for this problem.