Maximum Cardinality 1-Restricted Simple 2-Matchings

A simple 2-matching in a graph is a subgraph all of whose nodes have degree 1 or 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 min-max theorem for the maximum number of edges in a 1-restricted simple 2-matching. We prove this result constructively by presenting a polynomial time algorithm for finding a 1-restricted simple 2-matching with a maximum number of edges.

• Type: Journal
• Year: 2007
• Where: COMBINATORICS
• Authors: David Hartvigsen
• Keywords: COMBINATORICS 2007, Connected Component, Hamilton Cycle, Maximum Number