{"paper":{"title":"Enclosings of Decompositions of Complete Multigraphs in 2-Factorizations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Carl Feghali, Matthew Johnson","submitted_at":"2016-08-24T20:29:32Z","abstract_excerpt":"Let $k$, $\\lambda$ and $\\mu$ be positive integers. A decomposition of a multigraph $ \\lambda G$ into edge-disjoint subgraphs $G_1, \\ldots , G_k$ is said to be \\emph{enclosed} by a decomposition of a multigraph $\\mu H$ into edge-disjoint subgraphs $H_1, \\ldots , H_k$ if $\\mu > \\lambda$ and $G_i$ is a subgraph of $H_i$, $1 \\leq i \\leq k$. In this paper we initiate the study of when a decomposition can be enclosed by a decomposition that consists of spanning subgraphs.\n  A decomposition of a graph is a 2-factorization if each subgraph is 2-regular and is Hamiltonian if each subgraph is a Hamilton"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.06961","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"}