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Akitaya et al. give an algorithm to test whether $(G, \\mathcal{C})$ can be embedded onto $D_{\\mathcal C}$ with the additional constraint that edges are routed through a set of pipes between the disks. Based on such an embedding, we prove that every clustered graph and every disk arrangement without pipe-disk intersections has a planar stra"},"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":"1811.00785","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2018-11-02T09:05:43Z","cross_cats_sorted":["cs.DS"],"title_canon_sha256":"152f8e9699cee73f47167368ec941a1f7f1f62ef735e014368e5eff4a4da7a1a","abstract_canon_sha256":"b21274c60070fc266d145e0e75ebf6d47288071f8f18456af62ca9b685411266"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:01:42.157330Z","signature_b64":"c4LhS9wewYMnu/33izrfZLeDWgaWxU27XlKTZa5s451Qj72chxV3SbUoslQIszbVkPucK4hJwyG4oUfZ8aJ8AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"575ca632f499acb47aca88725c5aa6c3db6ddab480efbbafff6e5b92b17990f6","last_reissued_at":"2026-05-18T00:01:42.156693Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:01:42.156693Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Drawing Clustered Graphs on Disk Arrangements","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS"],"primary_cat":"cs.CG","authors_text":"Ignaz Rutter, Marcel Radermacher, Nina Zimbel, Tamara Mchedlidze","submitted_at":"2018-11-02T09:05:43Z","abstract_excerpt":"Let $G=(V, E)$ be a planar graph and let $\\mathcal{C}$ be a partition of $V$. 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