{"paper":{"title":"Labeled Packing of Non Star Tree into its Fifth Power and Sixth Power","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Amine El Sahili, Hamamache Kheddouci, Maidoun Mortada","submitted_at":"2013-02-18T10:48:27Z","abstract_excerpt":"In this paper we prove that we can find a labeled packing of a non star tree $T$ into $T^6$ with $m_T+\\lceil\\frac{n-m_T}{5}\\rceil$ labels, where $n$ is the number of vertices of $T$ and $m_T$ is the maximum number of leaves that can be removed from $T$ 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 $T$ into $T^5$ with $m_T+1$ labels and a labeled packing of a path $P_n$, $n\\geq 4$, into $P_n^4$ with $\\lceil \\frac{n}{4}\\rceil$ labels."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.4219","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}