{"paper":{"title":"Double-Star Decomposition of Regular Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Abbas Seify, Hamidreza Maimani, Saieed Akbari, Shahab Haghi","submitted_at":"2015-05-20T15:54:56Z","abstract_excerpt":"A tree containing exactly two non-pendant vertices is called a double-star. A double-star with degree sequence $(k_1+ 1, k_2+ 1, 1, \\ldots, 1)$ is denoted by $S_{k_1, k_2}$. We study the edge-decomposition of regular graphs into double-stars. It was proved that every double-star of size $k$ decomposes every $2k$-regular graph. In this paper, we extend this result to $(2k+ 1)$-regular graphs, by showing that every $(2k+ 1)$-regular graph containing two disjoint perfect matchings is decomposed into $S_{k_1, k_2}$ and $S_{k_{1}-1, k_2}$, for all positive integers $k_1$ and $k_2$ such that $k_1 + "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.05432","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"}