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 Kn. 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.

[1]  Seymour Schuster,et al.  Embedding (p,p−1) graphs in their complements , 1978 .

[2]  Mariusz Wozniak,et al.  On cyclically embeddable graphs , 1999, Discuss. Math. Graph Theory.

[3]  Mariusz Wozniak,et al.  Embedding Graphs of Small Size , 1994, Discret. Appl. Math..

[4]  B. Bollobás,et al.  Extremal Graph Theory , 2013 .

[5]  Hian Poh Yap,et al.  Packing of graphs - a survey , 1988, Discret. Math..

[6]  A. Pawel Wojda,et al.  Triple placement of graphs , 1993, Graphs Comb..

[7]  Mariusz Wozniak,et al.  On cyclically embeddable (n, n-1)-graphs , 2002, Discret. Math..

[8]  Hamamache Kheddouci,et al.  On the packing of three graphs , 2001, Discret. Math..

[9]  Mariusz Wozniak,et al.  Packing three trees , 1996, Discret. Math..

[10]  Hong Wang,et al.  Packing Three Copies of a Tree into a Complete Graph , 1993, Eur. J. Comb..

[11]  Mariusz Woźniak.  Packing of graphs , 1997 .

[12]  Mariusz Wozniak,et al.  On cyclically embeddable (n, n)-graphs , 2003, Discuss. Math. Graph Theory.

[13]  A. Pawel Wojda,et al.  On self-complementation , 1985, J. Graph Theory.

[14]  Hamamache Kheddouci,et al.  A note on the packing of two copies of some trees into their third power , 2003, Appl. Math. Lett..

[15]  David Burns,et al.  Every (p, p-2) graph is contained in its complement , 1977, J. Graph Theory.

[16]  Hamamache Kheddouci,et al.  Packing two copies of a tree into its fourth power , 2000, Discret. Math..

[17]  R. W. Robinson,et al.  Isomorphic factorisations. I. Complete graphs , 1978 .

[18]  C. R. J. Claphman.  Graphs self-complementary in K n -e , 1990 .

[19]  T. Gangopadhyay.  Packing graphs in their complements , 1998, Discret. Math..

[20]  C. R. J. Clapham.  Graphs self-complementary in Kn - e , 1990, Discret. Math..

[21]  Joel H. Spencer,et al.  Edge disjoint placement of graphs , 1978, J. Comb. Theory B.

[22]  A. Pawel Wojda,et al.  Erratum to "On self-complementary supergraphs of (n, n)-graphs" [Discrete Math. 292(2005) 167-185] , 2005, Discret. Math..

[23]  A. Pawel Wojda,et al.  On self-complementary supergraphs of (n, n)-graphs , 2005, Discret. Math..

[24]  Richard A. Gibbs.  Self-complementary graphs , 1974 .

[25]  Raphael Yuster,et al.  Packing Graphs: The packing problem solved , 1996, Electron. J. Comb..

[26]  Zdzislaw Skupien.  The complete grapht-packings andt-coverings , 1993, Graphs Comb..