{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:V2JNOOTKVHY5LIBEE634WVB3MG","short_pith_number":"pith:V2JNOOTK","schema_version":"1.0","canonical_sha256":"ae92d73a6aa9f1d5a02427b7cb543b618ebf592cc5157c9b875d1c30d695286d","source":{"kind":"arxiv","id":"1808.10137","version":1},"attestation_state":"computed","paper":{"title":"Recognizing Generating Subgraphs in Graphs without Cycles of Lengths 6 and 7","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","math.CO"],"primary_cat":"cs.CC","authors_text":"David Tankus","submitted_at":"2018-08-30T06:35:49Z","abstract_excerpt":"Let $B$ be an induced complete bipartite subgraph of $G$ on vertex sets of bipartition $B_{X}$ and $B_{Y}$. The subgraph $B$ is {\\it generating} if there exists an independent set $S$ such that each of $S \\cup B_{X}$ and $S \\cup B_{Y}$ is a maximal independent set in the graph. If $B$ is generating, it \\textit{produces} the restriction $w(B_{X})=w(B_{Y})$. Let $w:V(G) \\longrightarrow\\mathbb{R}$ be a weight function. We say that $G$ is $w$-well-covered if all maximal independent sets are of the same weight. The graph $G$ is $w$-well-covered if and only if $w$ satisfies all restrictions produced"},"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":"1808.10137","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2018-08-30T06:35:49Z","cross_cats_sorted":["cs.DM","math.CO"],"title_canon_sha256":"9c5bbd4c1ad06dcae1615fde2c07d1306f18c3fa0b3090595163291c031bbb74","abstract_canon_sha256":"a69d580cacec0300942c51cd7a6aefec7a9892f531b362f1136ee169ec2d89c5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:06:49.709131Z","signature_b64":"DsxyiNqAk/EZ5JFWT2kg1Pe65Lx0QvBllz/XbKpKfjwuffF4xy6lxONcFZQCN+4T8NKKgvSaOeVujD6nam6bBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ae92d73a6aa9f1d5a02427b7cb543b618ebf592cc5157c9b875d1c30d695286d","last_reissued_at":"2026-05-18T00:06:49.708388Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:06:49.708388Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Recognizing Generating Subgraphs in Graphs without Cycles of Lengths 6 and 7","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","math.CO"],"primary_cat":"cs.CC","authors_text":"David Tankus","submitted_at":"2018-08-30T06:35:49Z","abstract_excerpt":"Let $B$ be an induced complete bipartite subgraph of $G$ on vertex sets of bipartition $B_{X}$ and $B_{Y}$. The subgraph $B$ is {\\it generating} if there exists an independent set $S$ such that each of $S \\cup B_{X}$ and $S \\cup B_{Y}$ is a maximal independent set in the graph. If $B$ is generating, it \\textit{produces} the restriction $w(B_{X})=w(B_{Y})$. Let $w:V(G) \\longrightarrow\\mathbb{R}$ be a weight function. We say that $G$ is $w$-well-covered if all maximal independent sets are of the same weight. The graph $G$ is $w$-well-covered if and only if $w$ satisfies all restrictions produced"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.10137","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":"1808.10137","created_at":"2026-05-18T00:06:49.708492+00:00"},{"alias_kind":"arxiv_version","alias_value":"1808.10137v1","created_at":"2026-05-18T00:06:49.708492+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.10137","created_at":"2026-05-18T00:06:49.708492+00:00"},{"alias_kind":"pith_short_12","alias_value":"V2JNOOTKVHY5","created_at":"2026-05-18T12:32:56.356000+00:00"},{"alias_kind":"pith_short_16","alias_value":"V2JNOOTKVHY5LIBE","created_at":"2026-05-18T12:32:56.356000+00:00"},{"alias_kind":"pith_short_8","alias_value":"V2JNOOTK","created_at":"2026-05-18T12:32:56.356000+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/V2JNOOTKVHY5LIBEE634WVB3MG","json":"https://pith.science/pith/V2JNOOTKVHY5LIBEE634WVB3MG.json","graph_json":"https://pith.science/api/pith-number/V2JNOOTKVHY5LIBEE634WVB3MG/graph.json","events_json":"https://pith.science/api/pith-number/V2JNOOTKVHY5LIBEE634WVB3MG/events.json","paper":"https://pith.science/paper/V2JNOOTK"},"agent_actions":{"view_html":"https://pith.science/pith/V2JNOOTKVHY5LIBEE634WVB3MG","download_json":"https://pith.science/pith/V2JNOOTKVHY5LIBEE634WVB3MG.json","view_paper":"https://pith.science/paper/V2JNOOTK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1808.10137&json=true","fetch_graph":"https://pith.science/api/pith-number/V2JNOOTKVHY5LIBEE634WVB3MG/graph.json","fetch_events":"https://pith.science/api/pith-number/V2JNOOTKVHY5LIBEE634WVB3MG/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/V2JNOOTKVHY5LIBEE634WVB3MG/action/timestamp_anchor","attest_storage":"https://pith.science/pith/V2JNOOTKVHY5LIBEE634WVB3MG/action/storage_attestation","attest_author":"https://pith.science/pith/V2JNOOTKVHY5LIBEE634WVB3MG/action/author_attestation","sign_citation":"https://pith.science/pith/V2JNOOTKVHY5LIBEE634WVB3MG/action/citation_signature","submit_replication":"https://pith.science/pith/V2JNOOTKVHY5LIBEE634WVB3MG/action/replication_record"}},"created_at":"2026-05-18T00:06:49.708492+00:00","updated_at":"2026-05-18T00:06:49.708492+00:00"}