On distance-3 matchings and induced matchings Original Research Article

For a finite undirected graph image and positive integer image, an edge set image is a distance-k matching if the pairwise distance of edges in image is at least image in image. For image, this gives the usual notion of matching in graphs, and for general image, distance-image matchings were called k-separated matchings by Stockmeyer and Vazirani. The special case image has been studied under the names induced matching (i.e., a matching which forms an induced subgraph in image) by Cameron and strong matching by Golumbic and Laskar in various papers.