{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:WM45V3LHFNATUQADS4DNN2VQDH","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":"0de8bfacd1cf93b423fd257a034787a097c1c1780ae5d3a24735971f30ee1805","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-12-27T19:45:43Z","title_canon_sha256":"5e9207bfc6977fe26404846a8f508372f802c6eb7bcfece212edc6d315f371a2"},"schema_version":"1.0","source":{"id":"1812.10808","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.10808","created_at":"2026-05-17T23:57:17Z"},{"alias_kind":"arxiv_version","alias_value":"1812.10808v1","created_at":"2026-05-17T23:57:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.10808","created_at":"2026-05-17T23:57:17Z"},{"alias_kind":"pith_short_12","alias_value":"WM45V3LHFNAT","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_16","alias_value":"WM45V3LHFNATUQAD","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_8","alias_value":"WM45V3LH","created_at":"2026-05-18T12:33:01Z"}],"graph_snapshots":[{"event_id":"sha256:813bddffed09500e4fee63caf9819c3ff6c3cbdce8affff66d8536d78724ce3d","target":"graph","created_at":"2026-05-17T23:57:17Z","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":"In the vertex cover problem, the input is a graph $G$ and an integer $k$, and the goal is to decide whether there is a set of vertices $S$ of size at most $k$ such that every edge of $G$ is incident on at least one vertex in $S$. We study the vertex cover problem on graphs with maximum degree 4 and minimum degree at least 2, parameterized by $r = k-n/3$. We give an algorithm for this problem whose running time is $O^*(1.6253^r)$. As a corollary, we obtain an $O^*(1.2403^k)$-time algorithm for vertex cover on graphs with maximum degree 4.","authors_text":"Dekel Tsur","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-12-27T19:45:43Z","title":"Above guarantee parameterization for vertex cover on graphs with maximum degree 4"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.10808","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:d9f162b809acafd7407acbf177df4d3c680d232660564c75f0974343582b9789","target":"record","created_at":"2026-05-17T23:57:17Z","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":"0de8bfacd1cf93b423fd257a034787a097c1c1780ae5d3a24735971f30ee1805","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-12-27T19:45:43Z","title_canon_sha256":"5e9207bfc6977fe26404846a8f508372f802c6eb7bcfece212edc6d315f371a2"},"schema_version":"1.0","source":{"id":"1812.10808","kind":"arxiv","version":1}},"canonical_sha256":"b339daed672b413a40039706d6eab019dd882dd879775e2fb321257940e2d196","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b339daed672b413a40039706d6eab019dd882dd879775e2fb321257940e2d196","first_computed_at":"2026-05-17T23:57:17.015341Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:57:17.015341Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fn0m3DvVi8CJyRY5dlFRjhfMkivln8Cn2t4QLCLWOT0clDrJsZlATNIF6SzhiVXC/mw+Q1UVpMEX0XKfNj6+CQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:57:17.015807Z","signed_message":"canonical_sha256_bytes"},"source_id":"1812.10808","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d9f162b809acafd7407acbf177df4d3c680d232660564c75f0974343582b9789","sha256:813bddffed09500e4fee63caf9819c3ff6c3cbdce8affff66d8536d78724ce3d"],"state_sha256":"18f43596d84fdf45f98d3b5d0f2a003b11be139c4d8412edc75ef8c0cd5309f0"}