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Treewidth sparsifiers of degree $3$ are of particular interest, as routing on node-disjoint paths, and computing minors seems easier in sub-cubic graphs than in general graphs.\n  In this paper we describe an algorithm that, given a graph $G$ of treewidth $k$, computes a topological minor $H$ of $G$ such that (i) the treewidth of $H$ is $\\Omega(k/\\text{polylog}(k))$; (ii)","authors_text":"Chandra Chekuri, Julia Chuzhoy","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2014-10-04T03:37:29Z","title":"Degree-3 Treewidth Sparsifiers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.1016","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:69c039c9035c9ec1807fc9a0fac4751af753d7d104c354e90f3fb872326483ee","target":"record","created_at":"2026-05-18T02:41:02Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"c3b0d81dfb5b98f99cc400ac0155decf9fc14a3fc421b9f0ab18b81f6219279c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2014-10-04T03:37:29Z","title_canon_sha256":"334bcff116d44ba061f3ee39c8a6692a3312001d2f2bd6efc63895a9842f5034"},"schema_version":"1.0","source":{"id":"1410.1016","kind":"arxiv","version":1}},"canonical_sha256":"4e0dd08defb11cf28dcc09671615e20d0542c8bd60f7e42d317e4e91c60d8358","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4e0dd08defb11cf28dcc09671615e20d0542c8bd60f7e42d317e4e91c60d8358","first_computed_at":"2026-05-18T02:41:02.971336Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:41:02.971336Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"26AGk7nHcrPIMmUkpwHDcVxBeezKv4I5Ix558UpqL6vhJuX+sBm+VNqBzcj2eiw/7P2mJgJIWLZllCVJMEyZDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:41:02.972026Z","signed_message":"canonical_sha256_bytes"},"source_id":"1410.1016","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:69c039c9035c9ec1807fc9a0fac4751af753d7d104c354e90f3fb872326483ee","sha256:fb3ec3a424b3267cddf8675b3acafe889d4740f8598b847df8926b3cba00c6df"],"state_sha256":"5bea1048ab95268910ac44897e7253f169938ec4cffd4112ec5ffd5f4cef8209"}