Graph Packings

A matching of G can be viewed as a set of disjoint subgraphs of G each isomorphic to K2. A natural generalization is a set of disjoint subgraphs each isomorphic to a fixed graph H, or to a member of a fixed family H of graphs. This is a survey of such packing problems. It covers older work of Corneujols, Hartvigsen, and Pulleyblank, of Loebl and Poljak, and of Kirkpatrick and the author, and reports on new results of Kaneko, Kano, Katona, Kiralyi, Brewster, Pantel, Rizzi, Yeo, Hartvigsen, and the author. The emphasis is on illustrating the use of NP-completeness in ‘predicting’ good characterizations.