Let G = (V, G) be a graph on n vertices and let σ be such a permutation of the set of vertices V(G) that if an edge xy belongs to E(G) , then σ(x)σ(y) does not belong to E(G).
Then we say that there is a packing of two copies of a graph G into a complete graph Kn or an embedding of a graph G into its complement Ḡ. The permutation σ is called a packing permutation.
The fundamental question is: what conditions must satisfy a graph G so that two of its copies are packable?
It is easy to generalize the above problem in many different directions. Instead of two copies, one can consider three and more copies, instead of copies of the same graph one can consider packing two (or more) different graphs, or put additional conditions on the packing permutation.
The state of knowledge at the end of the last century is described, for example, in two survey papers "Packing of Graphs" and "Packing of graphs — some recent results and trends" and if we narrow the consideration to copies of the same graph, then also in the paper "Packing of graphs and permutations – a survey".