{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:YWRHNUYBMM6AP55LVR22QHRDDL","short_pith_number":"pith:YWRHNUYB","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"},"canonical_sha256":"c5a276d301633c07f7abac75a81e231ae3808a99585bbb1be53b750831c1a0db","source":{"kind":"arxiv","id":"1410.8807","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.8807","created_at":"2026-05-18T01:29:59Z"},{"alias_kind":"arxiv_version","alias_value":"1410.8807v3","created_at":"2026-05-18T01:29:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.8807","created_at":"2026-05-18T01:29:59Z"},{"alias_kind":"pith_short_12","alias_value":"YWRHNUYBMM6A","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_16","alias_value":"YWRHNUYBMM6AP55L","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_8","alias_value":"YWRHNUYB","created_at":"2026-05-18T12:28:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:YWRHNUYBMM6AP55LVR22QHRDDL","target":"record","payload":{"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"},"canonical_sha256":"c5a276d301633c07f7abac75a81e231ae3808a99585bbb1be53b750831c1a0db","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"},"source_kind":"arxiv","source_id":"1410.8807","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":"2026-05-18T01:29:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HTmgNMJUkJs+F8gaR+2780zznxoemvspNA2Mspj+45Z0xCCjbLHFOlTNoXB+eIzQBU3l0Vg8bkAa36R7yFADBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T05:38:00.739466Z"},"content_sha256":"08e9e5f57b5c79ce33c2c0b3b844f75be01fbccc854c7fc391db9a81fa6d44a8","schema_version":"1.0","event_id":"sha256:08e9e5f57b5c79ce33c2c0b3b844f75be01fbccc854c7fc391db9a81fa6d44a8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:YWRHNUYBMM6AP55LVR22QHRDDL","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:29:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pYcdsQtOjuyvAJrFnKwdOG7lHhqSyIci4nGEi/0ds0g3NxTAujOsFWj6YaT2s84R1Fmg+X/9q8tUg9rCmgC9AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T05:38:00.739806Z"},"content_sha256":"cfc70f7426e9dd5405854265c16f1a3c3b233f4dc087e1f01aaa21a32e81772d","schema_version":"1.0","event_id":"sha256:cfc70f7426e9dd5405854265c16f1a3c3b233f4dc087e1f01aaa21a32e81772d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YWRHNUYBMM6AP55LVR22QHRDDL/bundle.json","state_url":"https://pith.science/pith/YWRHNUYBMM6AP55LVR22QHRDDL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YWRHNUYBMM6AP55LVR22QHRDDL/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":"2026-06-20T05:38:00Z","links":{"resolver":"https://pith.science/pith/YWRHNUYBMM6AP55LVR22QHRDDL","bundle":"https://pith.science/pith/YWRHNUYBMM6AP55LVR22QHRDDL/bundle.json","state":"https://pith.science/pith/YWRHNUYBMM6AP55LVR22QHRDDL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YWRHNUYBMM6AP55LVR22QHRDDL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:YWRHNUYBMM6AP55LVR22QHRDDL","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":"10e682c31692ce8b89f839a84990a00c8468e1257d848581dff97febe0c70462","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-10-31T16:55:44Z","title_canon_sha256":"385402428b80683ff7029a3fe1b8a0504dbc2e3e54302d455c206b9ba6905f1e"},"schema_version":"1.0","source":{"id":"1410.8807","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.8807","created_at":"2026-05-18T01:29:59Z"},{"alias_kind":"arxiv_version","alias_value":"1410.8807v3","created_at":"2026-05-18T01:29:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.8807","created_at":"2026-05-18T01:29:59Z"},{"alias_kind":"pith_short_12","alias_value":"YWRHNUYBMM6A","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_16","alias_value":"YWRHNUYBMM6AP55L","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_8","alias_value":"YWRHNUYB","created_at":"2026-05-18T12:28:59Z"}],"graph_snapshots":[{"event_id":"sha256:cfc70f7426e9dd5405854265c16f1a3c3b233f4dc087e1f01aaa21a32e81772d","target":"graph","created_at":"2026-05-18T01:29:59Z","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":"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","authors_text":"Aparna Lakshmanan S., Csilla Bujt\\'as, Zsolt Tuza","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-10-31T16:55:44Z","title":"Induced cycles in triangle graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.8807","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":"sha256:08e9e5f57b5c79ce33c2c0b3b844f75be01fbccc854c7fc391db9a81fa6d44a8","target":"record","created_at":"2026-05-18T01:29:59Z","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":"10e682c31692ce8b89f839a84990a00c8468e1257d848581dff97febe0c70462","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-10-31T16:55:44Z","title_canon_sha256":"385402428b80683ff7029a3fe1b8a0504dbc2e3e54302d455c206b9ba6905f1e"},"schema_version":"1.0","source":{"id":"1410.8807","kind":"arxiv","version":3}},"canonical_sha256":"c5a276d301633c07f7abac75a81e231ae3808a99585bbb1be53b750831c1a0db","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c5a276d301633c07f7abac75a81e231ae3808a99585bbb1be53b750831c1a0db","first_computed_at":"2026-05-18T01:29:59.268383Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:29:59.268383Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mpcnn+EgGVACWmjGqWSSX+PvsCLSiMVs/I5qoHJWA+BmZMFshmMdC9dhBxDdsKqBlSw2hTdNLzjX8RjeuHO0DA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:29:59.268877Z","signed_message":"canonical_sha256_bytes"},"source_id":"1410.8807","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:08e9e5f57b5c79ce33c2c0b3b844f75be01fbccc854c7fc391db9a81fa6d44a8","sha256:cfc70f7426e9dd5405854265c16f1a3c3b233f4dc087e1f01aaa21a32e81772d"],"state_sha256":"4e95eeb1c12fd09cd142a88e7da3a6d85596b90b7ce5200cf8f6979ed6acb935"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MJXC1hKOJrV99dG5rR+NxxGRIjou7oDx4DBuaxJSs+Qeegei/A3kmKdSmhAI67ZUEuzZbY3L8+0zhxrjxxyfBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T05:38:00.741664Z","bundle_sha256":"38ac7eec148d75f187f637fd06fc386c4825e9fffb347c5e34bfc569bd5e9afb"}}