{"paper":{"title":"Partitioning a graph into highly connected subgraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Derrick Stolee, Michael Ferrara, Michitaka Furuya, N. Narayanan, Shinya Fujita, Valentin Borozan, Yannis Manoussakis","submitted_at":"2014-01-13T02:10:39Z","abstract_excerpt":"Given $k\\ge 1$, a $k$-proper partition of a graph $G$ is a partition ${\\mathcal P}$ of $V(G)$ such that each part $P$ of ${\\mathcal P}$ induces a $k$-connected subgraph of $G$. We prove that if $G$ is a graph of order $n$ such that $\\delta(G)\\ge \\sqrt{n}$, then $G$ has a $2$-proper partition with at most $n/\\delta(G)$ parts. The bounds on the number of parts and the minimum degree are both best possible. We then prove that If $G$ is a graph of order $n$ with minimum degree $\\delta(G)\\ge\\sqrt{c(k-1)n}$, where $c=\\frac{2123}{180}$, then $G$ has a $k$-proper partition into at most $\\frac{cn}{\\del"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.2696","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"}