{"paper":{"title":"Indecomposable $1$-factorizations of the complete multigraph $\\lambda K_{2n}$ for every $\\lambda\\leq 2n$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Gloria Rinaldi, Simona Bonvicini","submitted_at":"2016-11-10T08:54:40Z","abstract_excerpt":"A $1$-factorization of the complete multigraph $\\lambda K_{2n}$ is said to be indecomposable if it cannot be represented as the union of $1$-factorizations of $\\lambda_0 K_{2n}$ and $(\\lambda-\\lambda_0) K_{2n}$, where $\\lambda_0<\\lambda$. It is said to be simple if no $1$-factor is repeated. For every $n\\geq 9$ and for every $(n-2)/3\\leq\\lambda\\leq 2n$, we construct an indecomposable $1$-factorization of $\\lambda K_{2n}$ which is not simple. These $1$-factorizations provide simple and indecomposable $1$-factorizations of $\\lambda K_{2s}$ for every $s\\geq 18$ and $2\\leq\\lambda\\leq 2\\lfloor s/2\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.03221","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"}