{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:UU3LWHFJO5RR37JQS2U5XV4AOB","short_pith_number":"pith:UU3LWHFJ","canonical_record":{"source":{"id":"1806.02590","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2018-06-07T09:57:27Z","cross_cats_sorted":[],"title_canon_sha256":"1424edf3c6654a1d10acee2810affe3d9d4a40f617e20615b17a07c1081c98dc","abstract_canon_sha256":"cfcb535b4dd92ff18b658461e935bd999722abe624b89d0c102d622303f09a4a"},"schema_version":"1.0"},"canonical_sha256":"a536bb1ca977631dfd3096a9dbd780705340b47a4074f86a07107cb589f7c79c","source":{"kind":"arxiv","id":"1806.02590","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.02590","created_at":"2026-05-17T23:56:10Z"},{"alias_kind":"arxiv_version","alias_value":"1806.02590v3","created_at":"2026-05-17T23:56:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.02590","created_at":"2026-05-17T23:56:10Z"},{"alias_kind":"pith_short_12","alias_value":"UU3LWHFJO5RR","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_16","alias_value":"UU3LWHFJO5RR37JQ","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_8","alias_value":"UU3LWHFJ","created_at":"2026-05-18T12:32:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:UU3LWHFJO5RR37JQS2U5XV4AOB","target":"record","payload":{"canonical_record":{"source":{"id":"1806.02590","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2018-06-07T09:57:27Z","cross_cats_sorted":[],"title_canon_sha256":"1424edf3c6654a1d10acee2810affe3d9d4a40f617e20615b17a07c1081c98dc","abstract_canon_sha256":"cfcb535b4dd92ff18b658461e935bd999722abe624b89d0c102d622303f09a4a"},"schema_version":"1.0"},"canonical_sha256":"a536bb1ca977631dfd3096a9dbd780705340b47a4074f86a07107cb589f7c79c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:56:10.009452Z","signature_b64":"4/T57HyW+OOzTV0Vn7UmP+bB6HYGy+24RBDDcaOyUFUMiGKh+6Udp9kxuVxWxoTT4TleyVFVIPVgMpGoOwPPCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a536bb1ca977631dfd3096a9dbd780705340b47a4074f86a07107cb589f7c79c","last_reissued_at":"2026-05-17T23:56:10.008776Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:56:10.008776Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1806.02590","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:56:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oe7sJJrlIHSpJzw8Mj0z+i/VO0oxbbpilURBSvONEsKocdda1g/1iyF6tq0tXIErOhLKTZxk2XtUlN//Jg/aDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T00:21:31.530914Z"},"content_sha256":"18534b5f1dc7ce085aebc4c77c9b1970193d6cb745cbe62b416524dd2846e22d","schema_version":"1.0","event_id":"sha256:18534b5f1dc7ce085aebc4c77c9b1970193d6cb745cbe62b416524dd2846e22d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:UU3LWHFJO5RR37JQS2U5XV4AOB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Greedy domination on biclique-free graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DM","authors_text":"Sebastian Siebertz","submitted_at":"2018-06-07T09:57:27Z","abstract_excerpt":"The greedy algorithm for approximating dominating sets is a simple method that is known to compute an $(\\ln n+1)$-approximation of a minimum dominating set on any graph with $n$ vertices. We show that a small modification of the greedy algorithm can be used to compute an $O(t^2\\cdot \\ln k)$-approximation, where~$k$ is the size of a minimum dominating set, on graphs that exclude the complete bipartite graph $K_{t,t}$ as a subgraph."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.02590","kind":"arxiv","version":3},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:56:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ceUZhqjpo68dbD1ULz2vnlIdHfUXLtltUh439OxuvwjM+ThfHrNrblmYZZjsfJuif1Pv8x5QosVnYkuMNY3OAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T00:21:31.531526Z"},"content_sha256":"4326adad28c54afe890700919261bbd95337b429f278371320bfcf4cb9d6e36e","schema_version":"1.0","event_id":"sha256:4326adad28c54afe890700919261bbd95337b429f278371320bfcf4cb9d6e36e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UU3LWHFJO5RR37JQS2U5XV4AOB/bundle.json","state_url":"https://pith.science/pith/UU3LWHFJO5RR37JQS2U5XV4AOB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UU3LWHFJO5RR37JQS2U5XV4AOB/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-27T00:21:31Z","links":{"resolver":"https://pith.science/pith/UU3LWHFJO5RR37JQS2U5XV4AOB","bundle":"https://pith.science/pith/UU3LWHFJO5RR37JQS2U5XV4AOB/bundle.json","state":"https://pith.science/pith/UU3LWHFJO5RR37JQS2U5XV4AOB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UU3LWHFJO5RR37JQS2U5XV4AOB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:UU3LWHFJO5RR37JQS2U5XV4AOB","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":"cfcb535b4dd92ff18b658461e935bd999722abe624b89d0c102d622303f09a4a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2018-06-07T09:57:27Z","title_canon_sha256":"1424edf3c6654a1d10acee2810affe3d9d4a40f617e20615b17a07c1081c98dc"},"schema_version":"1.0","source":{"id":"1806.02590","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.02590","created_at":"2026-05-17T23:56:10Z"},{"alias_kind":"arxiv_version","alias_value":"1806.02590v3","created_at":"2026-05-17T23:56:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.02590","created_at":"2026-05-17T23:56:10Z"},{"alias_kind":"pith_short_12","alias_value":"UU3LWHFJO5RR","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_16","alias_value":"UU3LWHFJO5RR37JQ","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_8","alias_value":"UU3LWHFJ","created_at":"2026-05-18T12:32:56Z"}],"graph_snapshots":[{"event_id":"sha256:4326adad28c54afe890700919261bbd95337b429f278371320bfcf4cb9d6e36e","target":"graph","created_at":"2026-05-17T23:56:10Z","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":"The greedy algorithm for approximating dominating sets is a simple method that is known to compute an $(\\ln n+1)$-approximation of a minimum dominating set on any graph with $n$ vertices. We show that a small modification of the greedy algorithm can be used to compute an $O(t^2\\cdot \\ln k)$-approximation, where~$k$ is the size of a minimum dominating set, on graphs that exclude the complete bipartite graph $K_{t,t}$ as a subgraph.","authors_text":"Sebastian Siebertz","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2018-06-07T09:57:27Z","title":"Greedy domination on biclique-free graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.02590","kind":"arxiv","version":3},"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":"sha256:18534b5f1dc7ce085aebc4c77c9b1970193d6cb745cbe62b416524dd2846e22d","target":"record","created_at":"2026-05-17T23:56:10Z","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":"cfcb535b4dd92ff18b658461e935bd999722abe624b89d0c102d622303f09a4a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2018-06-07T09:57:27Z","title_canon_sha256":"1424edf3c6654a1d10acee2810affe3d9d4a40f617e20615b17a07c1081c98dc"},"schema_version":"1.0","source":{"id":"1806.02590","kind":"arxiv","version":3}},"canonical_sha256":"a536bb1ca977631dfd3096a9dbd780705340b47a4074f86a07107cb589f7c79c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a536bb1ca977631dfd3096a9dbd780705340b47a4074f86a07107cb589f7c79c","first_computed_at":"2026-05-17T23:56:10.008776Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:56:10.008776Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4/T57HyW+OOzTV0Vn7UmP+bB6HYGy+24RBDDcaOyUFUMiGKh+6Udp9kxuVxWxoTT4TleyVFVIPVgMpGoOwPPCw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:56:10.009452Z","signed_message":"canonical_sha256_bytes"},"source_id":"1806.02590","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:18534b5f1dc7ce085aebc4c77c9b1970193d6cb745cbe62b416524dd2846e22d","sha256:4326adad28c54afe890700919261bbd95337b429f278371320bfcf4cb9d6e36e"],"state_sha256":"67a60783d77594935e046854c5fb7f415fe499bda5c6b10d973b7f99b3b218e5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KYMh5jXyRWYQaW55rUhEWYjeSmBbFhQHaOLe+Fx65/krn1nNt1Wau/aQqCPlyqL1CTszmqDlkWKlF8S/54KBDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T00:21:31.534909Z","bundle_sha256":"ea8b32fe7ff8419b40354e7a48d5b6d15baef0e5cae78e20234ef277151dc1b6"}}