{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:DM6LC4JW6R6J2ALMR2UG2WZEFF","short_pith_number":"pith:DM6LC4JW","schema_version":"1.0","canonical_sha256":"1b3cb17136f47c9d016c8ea86d5b24297b970beec93724a10c53e53a133e444b","source":{"kind":"arxiv","id":"1512.02730","version":1},"attestation_state":"computed","paper":{"title":"Plane Bichromatic Trees of Low Degree","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CG","authors_text":"Ahmad Biniaz, Anil Maheshwari, Michiel Smid, Prosenjit Bose","submitted_at":"2015-12-09T02:51:42Z","abstract_excerpt":"Let $R$ and $B$ be two disjoint sets of points in the plane such that $|B|\\leqslant |R|$, and no three points of $R\\cup B$ are collinear. We show that the geometric complete bipartite graph $K(R,B)$ contains a non-crossing spanning tree whose maximum degree is at most $\\max\\left\\{3, \\left\\lceil \\frac{|R|-1}{|B|}\\right\\rceil + 1\\right\\}$; this is the best possible upper bound on the maximum degree. This solves an open problem posed by Abellanas et al. at the Graph Drawing Symposium, 1996."},"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":"1512.02730","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2015-12-09T02:51:42Z","cross_cats_sorted":[],"title_canon_sha256":"26e5294bc355d2efc906f00e1d54b0a5863f1aec1914cba9e52a63e27a534c5b","abstract_canon_sha256":"f46f0b1dfe113cfa8195466451068d664ff2f57338a56cc5b605b7a8bca16447"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:24:43.238385Z","signature_b64":"SOaurPdwPWq7u5oFXMM6UXAWKI54aOR4p1i+mnoZYC+1BYouSJ+mNQux/L4FPB/VMuQWqZ/TuhV5x8Rr3IHyCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1b3cb17136f47c9d016c8ea86d5b24297b970beec93724a10c53e53a133e444b","last_reissued_at":"2026-05-18T01:24:43.237984Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:24:43.237984Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Plane Bichromatic Trees of Low Degree","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CG","authors_text":"Ahmad Biniaz, Anil Maheshwari, Michiel Smid, Prosenjit Bose","submitted_at":"2015-12-09T02:51:42Z","abstract_excerpt":"Let $R$ and $B$ be two disjoint sets of points in the plane such that $|B|\\leqslant |R|$, and no three points of $R\\cup B$ are collinear. We show that the geometric complete bipartite graph $K(R,B)$ contains a non-crossing spanning tree whose maximum degree is at most $\\max\\left\\{3, \\left\\lceil \\frac{|R|-1}{|B|}\\right\\rceil + 1\\right\\}$; this is the best possible upper bound on the maximum degree. This solves an open problem posed by Abellanas et al. at the Graph Drawing Symposium, 1996."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.02730","kind":"arxiv","version":1},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1512.02730","created_at":"2026-05-18T01:24:43.238051+00:00"},{"alias_kind":"arxiv_version","alias_value":"1512.02730v1","created_at":"2026-05-18T01:24:43.238051+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.02730","created_at":"2026-05-18T01:24:43.238051+00:00"},{"alias_kind":"pith_short_12","alias_value":"DM6LC4JW6R6J","created_at":"2026-05-18T12:29:17.054201+00:00"},{"alias_kind":"pith_short_16","alias_value":"DM6LC4JW6R6J2ALM","created_at":"2026-05-18T12:29:17.054201+00:00"},{"alias_kind":"pith_short_8","alias_value":"DM6LC4JW","created_at":"2026-05-18T12:29:17.054201+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/DM6LC4JW6R6J2ALMR2UG2WZEFF","json":"https://pith.science/pith/DM6LC4JW6R6J2ALMR2UG2WZEFF.json","graph_json":"https://pith.science/api/pith-number/DM6LC4JW6R6J2ALMR2UG2WZEFF/graph.json","events_json":"https://pith.science/api/pith-number/DM6LC4JW6R6J2ALMR2UG2WZEFF/events.json","paper":"https://pith.science/paper/DM6LC4JW"},"agent_actions":{"view_html":"https://pith.science/pith/DM6LC4JW6R6J2ALMR2UG2WZEFF","download_json":"https://pith.science/pith/DM6LC4JW6R6J2ALMR2UG2WZEFF.json","view_paper":"https://pith.science/paper/DM6LC4JW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1512.02730&json=true","fetch_graph":"https://pith.science/api/pith-number/DM6LC4JW6R6J2ALMR2UG2WZEFF/graph.json","fetch_events":"https://pith.science/api/pith-number/DM6LC4JW6R6J2ALMR2UG2WZEFF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DM6LC4JW6R6J2ALMR2UG2WZEFF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DM6LC4JW6R6J2ALMR2UG2WZEFF/action/storage_attestation","attest_author":"https://pith.science/pith/DM6LC4JW6R6J2ALMR2UG2WZEFF/action/author_attestation","sign_citation":"https://pith.science/pith/DM6LC4JW6R6J2ALMR2UG2WZEFF/action/citation_signature","submit_replication":"https://pith.science/pith/DM6LC4JW6R6J2ALMR2UG2WZEFF/action/replication_record"}},"created_at":"2026-05-18T01:24:43.238051+00:00","updated_at":"2026-05-18T01:24:43.238051+00:00"}