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.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1188, author = {Christian Germain and Hamamache Kheddouci}, title = {On the packing of two copies of a caterpillar in its third power}, journal = {Discussiones Mathematicae Graph Theory}, volume = {23}, year = {2003}, pages = {105-115}, zbl = {1037.05040}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1188} }
Christian Germain; Hamamache Kheddouci. On the packing of two copies of a caterpillar in its third power. Discussiones Mathematicae Graph Theory, Tome 23 (2003) pp. 105-115. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1188/
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