Fixed-point-free embeddings of digraphs with small size

We prove that every digraph of order n and size at most 74n-81 is embeddable in its complement. Moreover, for such digraphs there are embeddings without fixed points.

[1]  P. Hall.  On Representatives of Subsets , 1935 .

[2]  Reinhard Diestel,et al.  Graph Theory , 1997 .

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

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

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

[6]  Béla Bollobás,et al.  Packings of graphs and applications to computational complexity , 1978, J. Comb. Theory, Ser. B.

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

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

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

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

[11]  A. Pawel Wojda,et al.  Embedding digraphs of small size , 1997, Discret. Math..