{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:AZW25D7NFSSD33UXJOI2KFEFBR","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"ed81b7fec7157e752b881c18c8992a8edab4b766426c603dd1e3f3b0edd66738","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2014-10-02T13:08:52Z","title_canon_sha256":"97122a1d2a7143880872db091ec7716003b584b9a4f09aaa30d5d68e2155634c"},"schema_version":"1.0","source":{"id":"1410.0540","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.0540","created_at":"2026-05-18T02:41:10Z"},{"alias_kind":"arxiv_version","alias_value":"1410.0540v1","created_at":"2026-05-18T02:41:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.0540","created_at":"2026-05-18T02:41:10Z"},{"alias_kind":"pith_short_12","alias_value":"AZW25D7NFSSD","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_16","alias_value":"AZW25D7NFSSD33UX","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_8","alias_value":"AZW25D7N","created_at":"2026-05-18T12:28:19Z"}],"graph_snapshots":[{"event_id":"sha256:76d17d9b28a91d900d284a7fe757a4c1a91f2824b8f766b706af54a7c706f089","target":"graph","created_at":"2026-05-18T02:41:10Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"Given a set $P$ of $n$ points in the plane, the order-$k$ Gabriel graph on $P$, denoted by $k$-$GG$, has an edge between two points $p$ and $q$ if and only if the closed disk with diameter $pq$ contains at most $k$ points of $P$, excluding $p$ and $q$. We study matching problems in $k$-$GG$ graphs. We show that a Euclidean bottleneck perfect matching of $P$ is contained in $10$-$GG$, but $8$-$GG$ may not have any Euclidean bottleneck perfect matching. In addition we show that $0$-$GG$ has a matching of size at least $\\frac{n-1}{4}$ and this bound is tight. We also prove that $1$-$GG$ has a mat","authors_text":"Ahmad Biniaz, Anil Maheshwari, Michiel Smid","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2014-10-02T13:08:52Z","title":"Matching in Gabriel Graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.0540","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":"sha256:701975e767a618efa5a44bfb09f3fd3012687a3dbe3214fa69aa9524f4141592","target":"record","created_at":"2026-05-18T02:41:10Z","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":"ed81b7fec7157e752b881c18c8992a8edab4b766426c603dd1e3f3b0edd66738","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2014-10-02T13:08:52Z","title_canon_sha256":"97122a1d2a7143880872db091ec7716003b584b9a4f09aaa30d5d68e2155634c"},"schema_version":"1.0","source":{"id":"1410.0540","kind":"arxiv","version":1}},"canonical_sha256":"066dae8fed2ca43dee974b91a514850c73cf1bc7e688788055ab054929e0165e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"066dae8fed2ca43dee974b91a514850c73cf1bc7e688788055ab054929e0165e","first_computed_at":"2026-05-18T02:41:10.788398Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:41:10.788398Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NLbxWOk9dYSbtCGpsxfVsjphWNAF9hJc5LA5KJuqKEyZEisWGxfdS/PZ24lWH/O5HkH5jPM5s3fNNn17W5BOBA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:41:10.788977Z","signed_message":"canonical_sha256_bytes"},"source_id":"1410.0540","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:701975e767a618efa5a44bfb09f3fd3012687a3dbe3214fa69aa9524f4141592","sha256:76d17d9b28a91d900d284a7fe757a4c1a91f2824b8f766b706af54a7c706f089"],"state_sha256":"473b523054f307eebfeeb34a7828a614a667b654f9bec743c3dc6a17585c651d"}