{"paper":{"title":"Decompositions of highly connected graphs into paths of length five","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"F\\'abio Botler, Guilherme O. Mota, Marcio T. I. Oshiro, Yoshiko Wakabayashi","submitted_at":"2015-05-16T18:54:26Z","abstract_excerpt":"We study the Decomposition Conjecture posed by Bar\\'at and Thomassen (2006), which states that for every tree $T$ there exists a natural number $k_T$ such that, if $G$ is a $k_T$-edge-connected graph and $|E(T)|$ divides $|E(G)|$, then $G$ admits a decomposition into copies of $T$. In a series of papers, Thomassen verified this conjecture for stars, some bistars, paths of length $3$, and paths whose length is a power of $2$. We verify the Decomposition Conjecture for paths of length $5$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.04309","kind":"arxiv","version":2},"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"}