ISSN 1234-3099 (print version)

ISSN 2083-5892 (electronic version)

Discussiones Mathematicae Graph Theory

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Discussiones Mathematicae Graph Theory


Discussiones Mathematicae Graph Theory 23(1) (2003) 85-104
DOI: 10.7151/dmgt.1187


Agnieszka Görlich, Monika Pilśniak and Mariusz Woźniak

Faculty of Applied Mathematics AGH
Department of Discrete Mathematics
al. Mickiewicza 30, 30-059 Kraków, Poland


An embedding of a simple graph G into its complement [`G] 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 the embeddable (n,n)-graphs. We prove that with few exceptions the corresponding permutation may be chosen as cyclic one.

Keywords: packing of graphs, cyclic permutation.

2000 Mathematics Subject Classification: 05C70, 05C35.


[1] B. Bollobás, Extremal Graph Theory (Academic Press, London, 1978).
[2] B. Bollobás and S.E. Eldridge, Packings of graphs and applications to computational complexity, J. Combin. Theory 25 (B) (1978) 105-124.
[3] 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.
[4] D. Burns and S. Schuster, Embedding (n,n−1) graphs in their complements, Israel J. Math. 30 (1978) 313-320, doi: 10.1007/BF02761996.
[5] 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.
[6] T. Gangopadhyay, Packing graphs in their complements, Discrete Math. 186 (1998) 117-124, doi: 10.1016/S0012-365X(97)00186-6.
[7] B. Ganter, J. Pelikan and L. Teirlinck, Small sprawling systems of equicardinal sets, Ars Combin. 4 (1977) 133-142.
[8] S. Schuster, Fixed-point-free embeddings of graphs in their complements, Internat. J. Math. & Math. Sci. 1 (1978) 335-338, doi: 10.1155/S0161171278000356.
[9] M. Woźniak, Packing of Graphs, Dissertationes Math. 362 (1997) pp.78.
[10] M. Woźniak, On cyclically embeddable graphs, Discuss. Math. Graph Theory 19 (1999) 241-248, doi: 10.7151/dmgt.1099.
[11] M. Woźniak, On cyclically embeddable (n,n−1)-graphs, Discrete Math. 251 (2002) 173-179.
[12] H.P. Yap, Some Topics In Graph Theory, London Mathematical Society, Lectures Notes Series 108 (Cambridge University Press, Cambridge, 1986).
[13] H.P. Yap, Packing of graphs - a survey, Discrete Math. 72 (1988) 395-404. 

Received 5 July 2001
Revised 4 March 2002