ArticleOriginal scientific text
Title
On cyclically embeddable graphs
Authors 1
Affiliations
- Faculty of Applied Mathematics AGH, Department of Discrete Mathematics, Al. Mickiewicza 30, 30-059 Kraków, Poland
Abstract
An embedding of a simple graph G into its complement G̅ 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). In this note we consider some families of embeddable graphs such that the corresponding permutation is cyclic.
Keywords
packing of graphs, unicyclic graphs, cyclic permutation
Bibliography
- B. Bollobás, Extremal Graph Theory (Academic Press, London, 1978).
- B. Bollobás and S.E. Eldridge, Packings of graphs and applications to computational complexity, J. Combin. Theory 25 (B) (1978) 105-124.
- D. Burns and S. Schuster, Every (p,p-2) graph is contained in its complement, J. Graph Theory 1 (1977) 277-279, doi: 10.1002/jgt.3190010308.
- D. Burns and S. Schuster, Embedding (n,n-1) graphs in their complements, Israel J. Math. 30 (1978) 313-320, doi: 10.1007/BF02761996.
- R.J. Faudree, C.C. Rousseau, R.H. Schelp and S. Schuster, Embedding graphs in their complements, Czechoslovak Math. J. 31:106 (1981) 53-62.
- T. Gangopadhyay, Packing graphs in their complements, Discrete Math. 186 (1998) 117-124, doi: 10.1016/S0012-365X(97)00186-6.
- B. Ganter, J. Pelikan and L. Teirlinck, Small sprawling systems of equicardinal sets, Ars Combinatoria 4 (1977) 133-142.
- N. Sauer and J. Spencer, Edge disjoint placement of graphs, J. Combin. Theory 25 (B) (1978) 295-302.
- S. Schuster, Fixed-point-free embeddings of graphs in their complements, Internat. J. Math. & Math. Sci. 1 (1978) 335-338, doi: 10.1155/S0161171278000356.
- M. Woźniak, Embedding graphs of small size, Discrete Applied Math. 51 (1994) 233-241, doi: 10.1016/0166-218X(94)90112-0.
- M. Woźniak, Packing three trees, Discrete Math. 150 (1996) 393-402, doi: 10.1016/0012-365X(95)00204-A.
- M. Woźniak, Packing of Graphs, Dissertationes Mathematicae 362 (1997) pp.78.
- H.P. Yap, Some Topics in Graph Theory (London Mathematical Society, Lectures Notes Series 108, Cambridge University Press, Cambridge 1986).
- H.P. Yap, Packing of graphs - a survey, Discrete Math. 72 (1988) 395-404, doi: 10.1016/0012-365X(88)90232-4.