{"paper":{"title":"Enclosings of Decompositions of Complete Multigraphs in $2$-Edge-Connected $r$-Factorizations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Carl Feghali, John Asplund, Pierre Charbit","submitted_at":"2018-10-29T18:38:41Z","abstract_excerpt":"A decomposition of a multigraph $G$ is a partition of its edges into subgraphs $G(1), \\ldots , G(k)$. It is called an $r$-factorization if every $G(i)$ is $r$-regular and spanning. If $G$ is a subgraph of $H$, a decomposition of $G$ is said to be enclosed in a decomposition of $H$ if, for every $1 \\leq i \\leq k$, $G(i)$ is a subgraph of $H(i)$.\n  Feghali and Johnson gave necessary and sufficient conditions for a given decomposition of $\\lambda K_n$ to be enclosed in some $2$-edge-connected $r$-factorization of $\\mu K_{m}$ for some range of values for the parameters $n$, $m$, $\\lambda$, $\\mu$, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.12340","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"}