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Packing three copies of a tree into its sixth power

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Abstract

A graph H of order n is said to be \(k-placeable\) into a graph G, having the same order n, if G contains k edge-disjoint copies of H. Kaneko et al. [9] proved that any non-star tree T is \(2-placeable\) into its third power \(T^3\). In this paper, we give a particular interest on the \(3-placement\) of a tree T into its sixth power \(T^6\).

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Acknowledgements

Authors gratefully thank professor Youssef Boudabbous for his constructive and important comments that he give us in ( [2]) during the development of this work.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science of Sfax, Soukra Road km 4, PO Box 802, 3018, Sfax, Tunisia

    Tarak Louleb & Mohamed Y. Sayar

  2. LIRIS UMR 5205, CNRS, University of Lyon, Claude Bernard Lyon 1 University, 43 Bd du 11 Novembre 1918, 69622, Villeurbanne, France

    Fairouz Beggas & Hamamache Kheddouci

Authors
  1. Tarak Louleb
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  2. Mohamed Y. Sayar
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  3. Fairouz Beggas
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  4. Hamamache Kheddouci
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Corresponding author

Correspondence to Mohamed Y. Sayar.

Additional information

Communicated by Sharad S Sane, PhD.

This work is partially supported by “Informatique théorique au Maghreb” PHC-Maghreb Campus-France Project.

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Louleb, T., Sayar, M.Y., Beggas, F. et al. Packing three copies of a tree into its sixth power. Indian J Pure Appl Math 52, 558–570 (2021). https://doi.org/10.1007/s13226-021-00060-5

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