A note on interconnecting matchings in graphs

We prove a sufficient condition for a graph G to have a matching that interconnects all the components of a disconnected spanning subgraph of G. The condition is derived from a recent extension of the Matroid intersection theorem due to Aharoni and Berger. We apply the result to the problem of the existence of a (spanning) 2-walk in sufficiently tough graphs.

• Type: Journal
• Year: 2006
• Where: DM
• Authors: Tomás Kaiser
• Keywords: Disconnected Spanning Subgraph, DM 2006, Matroid Intersection, Sufficient Condition