Fixed‐point‐free embeddings of graphs in their complements

Abstract

The following is proved: IfGis a labeled(p,p−2)graph wherep≥2, then there exists an isomorphic embeddingϕofGin its complementG¯such thatϕhas no fixed vertices. The extension to(p,p−1)graphs is also considered.

Fixed-point-free embeddings of digraphs with small size

“…Some improvement of Theorem 1 related to the structure of embeddings is proved in [10]. Hence we obtain that for at least n − 1 − 2 × 7 2 > 0 pairs of vertices v p , v u such that (v p ) = v u , the above defined permutation is an fpf-embedding of D. (III) Let us suppose that |N(z 1 )|=2.…”

A list version of graph packing

“…where permissible packings send X 1 onto X 2 and Y 1 onto Y 2 . The problem of fixed-point free embeddings, studied by Schuster in 1978, considers a different restriction to the original packing problem [7]. In this case, two edge disjoint copies of a graph G are placed into K n with the additional property that two copies of the same vertex must be mapped to different vertices in K n .…”

On Self-Complementary Cyclic Packing of Forests

“…The relationship between the property "to be embeddable" and the property "to be a subgraph of a self-complementary graph of the same order" was discussed in [1], [8], [9]. The structure of packing permutations was also studied in [3], [7] and [10].…”