{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:OCAI3D2THO52GBHAXHG4MYHJ5Z","short_pith_number":"pith:OCAI3D2T","schema_version":"1.0","canonical_sha256":"70808d8f533bbba304e0b9cdc660e9ee6a2d167b2131ef09b2a4b513371d1ef0","source":{"kind":"arxiv","id":"1202.6461","version":1},"attestation_state":"computed","paper":{"title":"The Minimum Number of Dependent Arcs and a Related Parameter of Generalized Mycielski Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Hsin-Hao Lai, Ko-Wei Lih","submitted_at":"2012-02-29T07:00:02Z","abstract_excerpt":"Let D be an acyclic orientation of the graph G. An arc of D is dependent if its reversal creates a directed cycle. Let m(G) denote the minimum number of dependent arcs over all acyclic orientations of G. For any k > 0, a generalized Mycielski graph M_k(G) of G is defined. Note that M_1(G) is the usual Mycielskian of G. We generalize results concerning m(M_1(G)) in K. L. Collins, K. Tysdal, J. Graph Theory, 46 (2004), 285-296, to m(M_k(G)). The underlying graph of a Hasse diagram is called a cover graph. Let c(G) denote the the minimum number of edges to be deleted from a graph G to get a cover"},"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":"1202.6461","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-02-29T07:00:02Z","cross_cats_sorted":[],"title_canon_sha256":"59530a715826acaa8a2b87764c57bbcfa0aa3e0e5ed361481f85ddb8630d3ff3","abstract_canon_sha256":"3146a5b935a8f619f0a59633777414ea58a658020c121685c14229e25832791f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:01:12.503226Z","signature_b64":"8Q88Vs8m6XQyTl/6Gsc+hh8UhgJMQiHkjwMsBX6LzlvK+/ldhi3NA878Ub38If5P+gJAFqXRFv2IaT3bHQEEBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"70808d8f533bbba304e0b9cdc660e9ee6a2d167b2131ef09b2a4b513371d1ef0","last_reissued_at":"2026-05-18T04:01:12.502677Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:01:12.502677Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Minimum Number of Dependent Arcs and a Related Parameter of Generalized Mycielski Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Hsin-Hao Lai, Ko-Wei Lih","submitted_at":"2012-02-29T07:00:02Z","abstract_excerpt":"Let D be an acyclic orientation of the graph G. An arc of D is dependent if its reversal creates a directed cycle. Let m(G) denote the minimum number of dependent arcs over all acyclic orientations of G. For any k > 0, a generalized Mycielski graph M_k(G) of G is defined. Note that M_1(G) is the usual Mycielskian of G. We generalize results concerning m(M_1(G)) in K. L. Collins, K. Tysdal, J. Graph Theory, 46 (2004), 285-296, to m(M_k(G)). The underlying graph of a Hasse diagram is called a cover graph. Let c(G) denote the the minimum number of edges to be deleted from a graph G to get a cover"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.6461","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":"1202.6461","created_at":"2026-05-18T04:01:12.502761+00:00"},{"alias_kind":"arxiv_version","alias_value":"1202.6461v1","created_at":"2026-05-18T04:01:12.502761+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.6461","created_at":"2026-05-18T04:01:12.502761+00:00"},{"alias_kind":"pith_short_12","alias_value":"OCAI3D2THO52","created_at":"2026-05-18T12:27:16.716162+00:00"},{"alias_kind":"pith_short_16","alias_value":"OCAI3D2THO52GBHA","created_at":"2026-05-18T12:27:16.716162+00:00"},{"alias_kind":"pith_short_8","alias_value":"OCAI3D2T","created_at":"2026-05-18T12:27:16.716162+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/OCAI3D2THO52GBHAXHG4MYHJ5Z","json":"https://pith.science/pith/OCAI3D2THO52GBHAXHG4MYHJ5Z.json","graph_json":"https://pith.science/api/pith-number/OCAI3D2THO52GBHAXHG4MYHJ5Z/graph.json","events_json":"https://pith.science/api/pith-number/OCAI3D2THO52GBHAXHG4MYHJ5Z/events.json","paper":"https://pith.science/paper/OCAI3D2T"},"agent_actions":{"view_html":"https://pith.science/pith/OCAI3D2THO52GBHAXHG4MYHJ5Z","download_json":"https://pith.science/pith/OCAI3D2THO52GBHAXHG4MYHJ5Z.json","view_paper":"https://pith.science/paper/OCAI3D2T","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1202.6461&json=true","fetch_graph":"https://pith.science/api/pith-number/OCAI3D2THO52GBHAXHG4MYHJ5Z/graph.json","fetch_events":"https://pith.science/api/pith-number/OCAI3D2THO52GBHAXHG4MYHJ5Z/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OCAI3D2THO52GBHAXHG4MYHJ5Z/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OCAI3D2THO52GBHAXHG4MYHJ5Z/action/storage_attestation","attest_author":"https://pith.science/pith/OCAI3D2THO52GBHAXHG4MYHJ5Z/action/author_attestation","sign_citation":"https://pith.science/pith/OCAI3D2THO52GBHAXHG4MYHJ5Z/action/citation_signature","submit_replication":"https://pith.science/pith/OCAI3D2THO52GBHAXHG4MYHJ5Z/action/replication_record"}},"created_at":"2026-05-18T04:01:12.502761+00:00","updated_at":"2026-05-18T04:01:12.502761+00:00"}