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Discussiones Mathematicae Graph Theory 23(1) (2003) 105-115
DOI: https://doi.org/10.7151/dmgt.1188

ON THE PACKING OF TWO COPIES OF A CATERPILLAR IN ITS THIRD POWER

Christian Germain and Hamamache Kheddouci

LE2I, FRE-CNRS 2309, Université de Bourgogne
B.P. 47870, 21078 Dijon Cedex, France
e-mail: CGermain@u-bourgogne.fr, KHeddouc@u-bourgogne.fr

Abstract

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, cater- pillar.

2000 Mathematics Subject Classification: 05C70 (05C05).

References

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Received 10 July 2001
Revised 5 July 2002