{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:YWRHNUYBMM6AP55LVR22QHRDDL","short_pith_number":"pith:YWRHNUYB","schema_version":"1.0","canonical_sha256":"c5a276d301633c07f7abac75a81e231ae3808a99585bbb1be53b750831c1a0db","source":{"kind":"arxiv","id":"1410.8807","version":3},"attestation_state":"computed","paper":{"title":"Induced cycles in triangle graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Aparna Lakshmanan S., Csilla Bujt\\'as, Zsolt Tuza","submitted_at":"2014-10-31T16:55:44Z","abstract_excerpt":"The triangle graph of a graph $G$, denoted by ${\\cal T}(G)$, is the graph whose vertices represent the triangles ($K_3$ subgraphs) of $G$, and two vertices of ${\\cal T}(G)$ are adjacent if and only if the corresponding triangles share an edge. In this paper, we characterize graphs whose triangle graph is a cycle and then extend the result to obtain a characterization of $C_n$-free triangle graphs. As a consequence, we give a forbidden subgraph characterization of graphs $G$ for which ${\\cal T}(G)$ is a tree, a chordal graph, or a perfect graph. For the class of graphs whose triangle graph is p"},"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":"1410.8807","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-10-31T16:55:44Z","cross_cats_sorted":[],"title_canon_sha256":"385402428b80683ff7029a3fe1b8a0504dbc2e3e54302d455c206b9ba6905f1e","abstract_canon_sha256":"10e682c31692ce8b89f839a84990a00c8468e1257d848581dff97febe0c70462"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:29:59.268877Z","signature_b64":"mpcnn+EgGVACWmjGqWSSX+PvsCLSiMVs/I5qoHJWA+BmZMFshmMdC9dhBxDdsKqBlSw2hTdNLzjX8RjeuHO0DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c5a276d301633c07f7abac75a81e231ae3808a99585bbb1be53b750831c1a0db","last_reissued_at":"2026-05-18T01:29:59.268383Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:29:59.268383Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Induced cycles in triangle graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Aparna Lakshmanan S., Csilla Bujt\\'as, Zsolt Tuza","submitted_at":"2014-10-31T16:55:44Z","abstract_excerpt":"The triangle graph of a graph $G$, denoted by ${\\cal T}(G)$, is the graph whose vertices represent the triangles ($K_3$ subgraphs) of $G$, and two vertices of ${\\cal T}(G)$ are adjacent if and only if the corresponding triangles share an edge. In this paper, we characterize graphs whose triangle graph is a cycle and then extend the result to obtain a characterization of $C_n$-free triangle graphs. As a consequence, we give a forbidden subgraph characterization of graphs $G$ for which ${\\cal T}(G)$ is a tree, a chordal graph, or a perfect graph. For the class of graphs whose triangle graph is p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.8807","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1410.8807","created_at":"2026-05-18T01:29:59.268460+00:00"},{"alias_kind":"arxiv_version","alias_value":"1410.8807v3","created_at":"2026-05-18T01:29:59.268460+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.8807","created_at":"2026-05-18T01:29:59.268460+00:00"},{"alias_kind":"pith_short_12","alias_value":"YWRHNUYBMM6A","created_at":"2026-05-18T12:28:59.999130+00:00"},{"alias_kind":"pith_short_16","alias_value":"YWRHNUYBMM6AP55L","created_at":"2026-05-18T12:28:59.999130+00:00"},{"alias_kind":"pith_short_8","alias_value":"YWRHNUYB","created_at":"2026-05-18T12:28:59.999130+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/YWRHNUYBMM6AP55LVR22QHRDDL","json":"https://pith.science/pith/YWRHNUYBMM6AP55LVR22QHRDDL.json","graph_json":"https://pith.science/api/pith-number/YWRHNUYBMM6AP55LVR22QHRDDL/graph.json","events_json":"https://pith.science/api/pith-number/YWRHNUYBMM6AP55LVR22QHRDDL/events.json","paper":"https://pith.science/paper/YWRHNUYB"},"agent_actions":{"view_html":"https://pith.science/pith/YWRHNUYBMM6AP55LVR22QHRDDL","download_json":"https://pith.science/pith/YWRHNUYBMM6AP55LVR22QHRDDL.json","view_paper":"https://pith.science/paper/YWRHNUYB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1410.8807&json=true","fetch_graph":"https://pith.science/api/pith-number/YWRHNUYBMM6AP55LVR22QHRDDL/graph.json","fetch_events":"https://pith.science/api/pith-number/YWRHNUYBMM6AP55LVR22QHRDDL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YWRHNUYBMM6AP55LVR22QHRDDL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YWRHNUYBMM6AP55LVR22QHRDDL/action/storage_attestation","attest_author":"https://pith.science/pith/YWRHNUYBMM6AP55LVR22QHRDDL/action/author_attestation","sign_citation":"https://pith.science/pith/YWRHNUYBMM6AP55LVR22QHRDDL/action/citation_signature","submit_replication":"https://pith.science/pith/YWRHNUYBMM6AP55LVR22QHRDDL/action/replication_record"}},"created_at":"2026-05-18T01:29:59.268460+00:00","updated_at":"2026-05-18T01:29:59.268460+00:00"}