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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1401.2696","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-01-13T02:10:39Z","cross_cats_sorted":[],"title_canon_sha256":"70a463be5cd1249e38d9a66d8df08f7401fca9778e282e6d101075bf5c1cae89","abstract_canon_sha256":"07baa98cbc5ec88a16f067a307e3777b4ba95db4495601a315407b9ea772315b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:36:20.897275Z","signature_b64":"cjIZRQzaqycu7Z43tsbbTWk833hxr3A34LHl/bXUTK0ObnrZhxMxiL/d8mw62kvE2JIL6ruYaiJ5ipSq1ttyCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6ae9519869c591fd1e24399653e5558b6662e4ab476b48803a7d69cfc6a0c641","last_reissued_at":"2026-05-18T01:36:20.896742Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:36:20.896742Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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. 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