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. © 2006 Elsevier B.V. All rights reserved.
Kaiser, T. (2006). A note on interconnecting matchings in graphs. Discrete Mathematics, 306(18), 2245–2250. https://doi.org/10.1016/j.disc.2006.05.011