Labeled Packing of Non Star Tree into its Fifth Power and Sixth Power
Amine El Sahili, Hamamache Kheddouci, Maidoun Mortada

TL;DR
This paper establishes new bounds for labeled packings of non star trees into their fifth and sixth powers, improving understanding of graph packing with specific label constraints.
Contribution
It introduces novel bounds for labeled packings of non star trees into their fifth and sixth powers, extending previous graph packing results.
Findings
Labeled packing of non star trees into T^6 with m_T + ceil((n - m_T)/5) labels.
Labeled packing of non star trees into T^5 with m_T + 1 labels.
Labeled packing of paths into their fourth power with ceil(n/4) labels.
Abstract
In this paper we prove that we can find a labeled packing of a non star tree into with labels, where is the number of vertices of and is the maximum number of leaves that can be removed from in such a way that the obtained graph is a non star tree. Also, we prove that we can find a labeled packing of a non star tree into with labels and a labeled packing of a path , , into with labels.
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Taxonomy
TopicsLimits and Structures in Graph Theory · Advanced Graph Theory Research · Graph Labeling and Dimension Problems
