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The objective is to partition $G$ into $(V_1,V_2)$ such that $G[V_1]$ and $G[V_2]$ are connected, $|p(V_1)|,|p(V_2)|\\leq c_p$, and $\\max\\{\\frac{|V_1|}{|V_2|},\\frac{|V_2|}{|V_1|}\\}\\leq c_s$, for some constants $c_p$ and $c_s$. When $G$ is 2-connected, we show that a solution with $c_p=1$ and $c_s=3$ always exists and can be found in polynomial time. Moreover, when $G$ i"},"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":"1607.06509","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-07-21T21:24:00Z","cross_cats_sorted":["cs.CC","cs.DM","cs.DS"],"title_canon_sha256":"ea42213b8f519bc63d10626471b1a7533b692d040959f7a742576562cb5a24f7","abstract_canon_sha256":"12db11f5f46227226cd22b861457a67b03eb4ce1c72287dfc8dfd613e6200d30"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:10:41.603245Z","signature_b64":"cxIZZvp/NjKJQJruWFHNe7New7AmNXSn8B8TFpGzlLoj2j9my1tS+g61nm6EHK0PAF1t+n0ABgHDfhov6EKtDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"698ae3af878d6515639d5b15ed34d8f327700c746933ebd1a6819890b208b8e7","last_reissued_at":"2026-05-18T01:10:41.602824Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:10:41.602824Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Doubly Balanced Connected Graph Partitioning","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","cs.DM","cs.DS"],"primary_cat":"math.CO","authors_text":"Gil Zussman, Mihalis Yannakakis, Saleh Soltan","submitted_at":"2016-07-21T21:24:00Z","abstract_excerpt":"We introduce and study the Doubly Balanced Connected graph Partitioning (DBCP) problem: Let $G=(V,E)$ be a connected graph with a weight (supply/demand) function $p:V\\rightarrow \\{-1,+1\\}$ satisfying $p(V)=\\sum_{j\\in V} p(j)=0$. The objective is to partition $G$ into $(V_1,V_2)$ such that $G[V_1]$ and $G[V_2]$ are connected, $|p(V_1)|,|p(V_2)|\\leq c_p$, and $\\max\\{\\frac{|V_1|}{|V_2|},\\frac{|V_2|}{|V_1|}\\}\\leq c_s$, for some constants $c_p$ and $c_s$. When $G$ is 2-connected, we show that a solution with $c_p=1$ and $c_s=3$ always exists and can be found in polynomial time. 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