Geodesic
On the packing of two copies of a caterpillar in its third power
Discussiones Mathematicae. Graph Theory, Tome 23 (2003) no. 1, pp. 105-115

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H. Kheddouci, J.F. Saclé and M. Woźniak conjectured in 2000 that if a tree T is not a star, then there is an edge-disjoint placement of T into its third power.In this paper, we prove the conjecture for caterpillars.
Keywords: packing, placement, permutation, power of tree, caterpillar 
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Germain, Christian; Kheddouci, Hamamache. On the packing of two copies of a caterpillar in its third power. Discussiones Mathematicae. Graph Theory, Tome 23 (2003) no. 1, pp. 105-115. http://geodesic.mathdoc.fr/item/DMGT_2003_23_1_a6/