Geodesic
A note on careful packing of a graph
Discussiones Mathematicae. Graph Theory, Tome 15 (1995) no. 1, pp. 43-50

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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 
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Woźniak, M. A note on careful packing of a graph. Discussiones Mathematicae. Graph Theory, Tome 15 (1995) no. 1, pp. 43-50. http://geodesic.mathdoc.fr/item/DMGT_1995_15_1_a4/