Packing of graphs and permutations—a survey

Abstract

An embedding of a graph G (into its complement Ḡ) is a permutation σ on V(G) such that if an edge xy belongs to E(G) then σ(x)σ(y) does not belong to E(G). If there exists an embedding of G we say that G is embeddable or that there is a packing of two copies of the graph G into complete graph K_n. In this paper we discuss a variety of results, some quite recent, concerning the relationships between the embeddings of graphs in their complements and the structure of the embedding permutations.