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.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1005,
author = {M. Wo\'zniak},
title = {A note on careful packing of a graph},
journal = {Discussiones Mathematicae Graph Theory},
volume = {15},
year = {1995},
pages = {43-50},
zbl = {0831.05054},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1005}
}
M. Woźniak. A note on careful packing of a graph. Discussiones Mathematicae Graph Theory, Tome 15 (1995) pp. 43-50. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1005/
[000] [1] B. Bollobás, Extremal Graph Theory (Academic Press, London, 1978).
[001] [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. | Zbl 0387.05020
[002] [3] J.A. Bondy and U.S.R. Murty, Graph Theory with Applications, (North-Holland, New York, 1976). | Zbl 1226.05083
[003] [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. | Zbl 0375.05046
[004] [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. | Zbl 0379.05023
[005] [6] B. Ganter, J. Pelikan and L. Teirlinck, Small sprawling systems of equicardinal sets, Ars Combinatoria 4 (1977) 133-142. | Zbl 0418.05003
[006] [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. | Zbl 0417.05037
[007] [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. | Zbl 0767.05046
[008] [9] M. Woźniak, Embedding graphs of small size, Discrete Applied Math. 51 (1994) 233-241, doi: 10.1016/0166-218X(94)90112-0. | Zbl 0807.05025
[009] [10] M. Woźniak and A.P. Wojda, Triple placement of graphs, Graphs and Combinatorics 9 (1993) 85-91, doi: 10.1007/BF01195330. | Zbl 0817.05034
[010] [11] H.P. Yap, Some Topics In Graph Theory (London Mathematical Society, Lectures Notes Series 108, Cambridge University Press, Cambridge 1986). | Zbl 0588.05002
[011] [12] H.P. Yap, Packing of graphs - a survey, Discrete Math. 72 (1988) 395-404, doi: 10.1016/0012-365X(88)90232-4. | Zbl 0685.05036