{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:XJYK4D35WFTT4OMV3JIFXPNHMZ","short_pith_number":"pith:XJYK4D35","canonical_record":{"source":{"id":"1012.0012","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2010-11-30T21:05:40Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"80deb73a1a10c08a036b2d2e2862aa386d5f0e8c226ba5b2809b23b996479621","abstract_canon_sha256":"54067bff160d2c2a7ff70e28723b69c5ccbc00269c00a9cefbe2cf30be5c0287"},"schema_version":"1.0"},"canonical_sha256":"ba70ae0f7db1673e3995da505bbda7665c93b6e047225548d44ffc9f583ff2a2","source":{"kind":"arxiv","id":"1012.0012","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1012.0012","created_at":"2026-05-17T23:56:25Z"},{"alias_kind":"arxiv_version","alias_value":"1012.0012v3","created_at":"2026-05-17T23:56:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.0012","created_at":"2026-05-17T23:56:25Z"},{"alias_kind":"pith_short_12","alias_value":"XJYK4D35WFTT","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_16","alias_value":"XJYK4D35WFTT4OMV","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_8","alias_value":"XJYK4D35","created_at":"2026-05-18T12:26:17Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:XJYK4D35WFTT4OMV3JIFXPNHMZ","target":"record","payload":{"canonical_record":{"source":{"id":"1012.0012","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2010-11-30T21:05:40Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"80deb73a1a10c08a036b2d2e2862aa386d5f0e8c226ba5b2809b23b996479621","abstract_canon_sha256":"54067bff160d2c2a7ff70e28723b69c5ccbc00269c00a9cefbe2cf30be5c0287"},"schema_version":"1.0"},"canonical_sha256":"ba70ae0f7db1673e3995da505bbda7665c93b6e047225548d44ffc9f583ff2a2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:56:25.493065Z","signature_b64":"lwC0KUAsaloWq9EW09zQbkbEOsF26qH3UcR+7NAVahEFfvKjzqZfEbOJZafnvzuThu4KLzHD3TDQlzy7z4IODw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ba70ae0f7db1673e3995da505bbda7665c93b6e047225548d44ffc9f583ff2a2","last_reissued_at":"2026-05-17T23:56:25.492672Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:56:25.492672Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1012.0012","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":"2026-05-17T23:56:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Gj9U2sLar3GyvzXWNJz78p2K8wbe6TBR9Bph8952kbU1OjTRfhutExctIGDTZb7npAxrEqqeVlLDSpqbA+/xBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T05:26:09.806416Z"},"content_sha256":"ff632501a6d57cc192c0ae24c86bcc5b1cabe0836b9db63cda67fa07c572c417","schema_version":"1.0","event_id":"sha256:ff632501a6d57cc192c0ae24c86bcc5b1cabe0836b9db63cda67fa07c572c417"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:XJYK4D35WFTT4OMV3JIFXPNHMZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Domination When the Stars Are Out","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"cs.DS","authors_text":"Danny Hermelin, Erik Jan van Leeuwen, Gerhard Woeginger, Matthias Mnich","submitted_at":"2010-11-30T21:05:40Z","abstract_excerpt":"We algorithmize the recent structural characterization for claw-free graphs by Chudnovsky and Seymour. Building on this result, we show that Dominating Set on claw-free graphs is (i) fixed-parameter tractable and (ii) even possesses a polynomial kernel. To complement these results, we establish that Dominating Set is not fixed-parameter tractable on the slightly larger class of graphs that exclude K_{1,4} as an induced subgraph (K_{1,4}-free graphs). We show that our algorithmization can also be used to show that the related Connected Dominating Set problem is fixed-parameter tractable on claw"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.0012","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":"2026-05-17T23:56:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"azYf0KP9HVzMbCBs0I/yZJ04lo0pAdlSPArlAjgQ2e5RiSX9VThwnbVGnOYAAeDLcO2jV/oSuxkm2DdUjdSaDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T05:26:09.806811Z"},"content_sha256":"0699a2e83854b4976ed7009f8c560ffa6305dff23fac99cb9070f07235ad0d30","schema_version":"1.0","event_id":"sha256:0699a2e83854b4976ed7009f8c560ffa6305dff23fac99cb9070f07235ad0d30"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XJYK4D35WFTT4OMV3JIFXPNHMZ/bundle.json","state_url":"https://pith.science/pith/XJYK4D35WFTT4OMV3JIFXPNHMZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XJYK4D35WFTT4OMV3JIFXPNHMZ/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":"2026-05-30T05:26:09Z","links":{"resolver":"https://pith.science/pith/XJYK4D35WFTT4OMV3JIFXPNHMZ","bundle":"https://pith.science/pith/XJYK4D35WFTT4OMV3JIFXPNHMZ/bundle.json","state":"https://pith.science/pith/XJYK4D35WFTT4OMV3JIFXPNHMZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XJYK4D35WFTT4OMV3JIFXPNHMZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:XJYK4D35WFTT4OMV3JIFXPNHMZ","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":"54067bff160d2c2a7ff70e28723b69c5ccbc00269c00a9cefbe2cf30be5c0287","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2010-11-30T21:05:40Z","title_canon_sha256":"80deb73a1a10c08a036b2d2e2862aa386d5f0e8c226ba5b2809b23b996479621"},"schema_version":"1.0","source":{"id":"1012.0012","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1012.0012","created_at":"2026-05-17T23:56:25Z"},{"alias_kind":"arxiv_version","alias_value":"1012.0012v3","created_at":"2026-05-17T23:56:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.0012","created_at":"2026-05-17T23:56:25Z"},{"alias_kind":"pith_short_12","alias_value":"XJYK4D35WFTT","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_16","alias_value":"XJYK4D35WFTT4OMV","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_8","alias_value":"XJYK4D35","created_at":"2026-05-18T12:26:17Z"}],"graph_snapshots":[{"event_id":"sha256:0699a2e83854b4976ed7009f8c560ffa6305dff23fac99cb9070f07235ad0d30","target":"graph","created_at":"2026-05-17T23:56:25Z","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":"We algorithmize the recent structural characterization for claw-free graphs by Chudnovsky and Seymour. Building on this result, we show that Dominating Set on claw-free graphs is (i) fixed-parameter tractable and (ii) even possesses a polynomial kernel. To complement these results, we establish that Dominating Set is not fixed-parameter tractable on the slightly larger class of graphs that exclude K_{1,4} as an induced subgraph (K_{1,4}-free graphs). We show that our algorithmization can also be used to show that the related Connected Dominating Set problem is fixed-parameter tractable on claw","authors_text":"Danny Hermelin, Erik Jan van Leeuwen, Gerhard Woeginger, Matthias Mnich","cross_cats":["cs.DM"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2010-11-30T21:05:40Z","title":"Domination When the Stars Are Out"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.0012","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:ff632501a6d57cc192c0ae24c86bcc5b1cabe0836b9db63cda67fa07c572c417","target":"record","created_at":"2026-05-17T23:56:25Z","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":"54067bff160d2c2a7ff70e28723b69c5ccbc00269c00a9cefbe2cf30be5c0287","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2010-11-30T21:05:40Z","title_canon_sha256":"80deb73a1a10c08a036b2d2e2862aa386d5f0e8c226ba5b2809b23b996479621"},"schema_version":"1.0","source":{"id":"1012.0012","kind":"arxiv","version":3}},"canonical_sha256":"ba70ae0f7db1673e3995da505bbda7665c93b6e047225548d44ffc9f583ff2a2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ba70ae0f7db1673e3995da505bbda7665c93b6e047225548d44ffc9f583ff2a2","first_computed_at":"2026-05-17T23:56:25.492672Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:56:25.492672Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lwC0KUAsaloWq9EW09zQbkbEOsF26qH3UcR+7NAVahEFfvKjzqZfEbOJZafnvzuThu4KLzHD3TDQlzy7z4IODw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:56:25.493065Z","signed_message":"canonical_sha256_bytes"},"source_id":"1012.0012","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ff632501a6d57cc192c0ae24c86bcc5b1cabe0836b9db63cda67fa07c572c417","sha256:0699a2e83854b4976ed7009f8c560ffa6305dff23fac99cb9070f07235ad0d30"],"state_sha256":"d161d7d527d57a1481888884883ad0e1c42b3a471a3d5905324cdf71f6ec5009"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"G0KB3L4sSDyHZv1szyh4mi6HNxK7ZTzrdtGBxU24RTmDsRYgzz6AGcwcD4ovUw9x9I5xL0o4Z6FJ0JVxCXV/AA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T05:26:09.809959Z","bundle_sha256":"365de952ab1b6a589b349913332f4513c956e7a79d005aa0c21c365fa348df35"}}