DMGT

ISSN 1234-3099 (print version)

ISSN 2083-5892 (electronic version)

https://doi.org/10.7151/dmgt

Discussiones Mathematicae Graph Theory

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Discussiones Mathematicae Graph Theory

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Discussiones Mathematicae Graph Theory  15(1) (1995)   43-50
DOI: https://doi.org/10.7151/dmgt.1005

A NOTE ON CAREFUL PACKING OF A GRAPH

M. Woźniak

Instytut Matematyki AGH
al. Mickiewicza 30, 30-059 Kraków, Poland

Abstract

Let  G be a simple graph of order  n and size  e(G). It is well known that if  e(G) ≤ n-2, then there is an edge-disjoint placement of two copies of  G into  Kn. We prove that with the same condition on size of  G   we have actually (with few exceptions) a careful packing of  G, that is an edge-disjoint placement of two copies of  G   into  Kn∖Cn.

Keywords: pucking of graphs

1991 Mathematics Subject Classification: 05C70

References

[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 (B) 25 (1978) 105-124, doi: 10.1016/0095-8956(78)90030-8.
[3] J.A. Bondy and U.S.R. Murty, Graph Theory with Applications, (North-Holland, New York, 1976).
[4] 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.
[5] D. Burns and S. Schuster, Embedding   (n,n-1)- graphs in their complements, Israel J. Math. 30 (1978) 313-320, doi: 10.1007/BF02761996.
[6] B. Ganter, J. Pelikan and L. Teirlinck, Small sprawling systems of equicardinal sets, Ars Combinatoria 4 (1977) 133-142.
[7] N. Sauer and J. Spencer, Edge disjoint placement of graphs, J. Combin Theory (B) 25 (1978) 295-302, doi: 10.1016/0095-8956(78)90005-9.
[8] M. Woźniak, Embedding of graphs in the complements of their squares, in: J. Nesset ril and M. Fiedler, eds, Fourth Czechoslovakian Symp. on Combinatorics, Graphs and Complexity, (Elsevier Science Publishers B.V.,1992) 345-349.
[9] M. Woźniak, Embedding graphs of small size, Discrete Applied Math. 51 (1994) 233-241, doi: 10.1016/0166-218X(94)90112-0.
[10] M. Woźniak and A.P. Wojda, Triple placement of graphs, Graphs and Combinatorics 9 (1993) 85-91, doi: 10.1007/BF01195330.
[11] H.P. Yap, Some Topics In Graph Theory (London Mathematical Society, Lectures Notes Series 108, Cambridge University Press, Cambridge 1986).
[12] H.P. Yap, Packing of graphs - a survey, Discrete Math. 72 (1988) 395-404, doi: 10.1016/0012-365X(88)90232-4.
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