{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:EDBRHBBVMD4AVJBZK5XJL6HSGY","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":"735462355a3df50ac1b6fb6d904392561a011a90190e11b110fc26a3cc2a3bc2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-02-13T19:54:20Z","title_canon_sha256":"67e236eea1fb5e3ecbda783a37b57ca0a3cef3f7435a04c0501a5d8e56442a74"},"schema_version":"1.0","source":{"id":"1602.04370","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.04370","created_at":"2026-05-18T01:20:51Z"},{"alias_kind":"arxiv_version","alias_value":"1602.04370v1","created_at":"2026-05-18T01:20:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.04370","created_at":"2026-05-18T01:20:51Z"},{"alias_kind":"pith_short_12","alias_value":"EDBRHBBVMD4A","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_16","alias_value":"EDBRHBBVMD4AVJBZ","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_8","alias_value":"EDBRHBBV","created_at":"2026-05-18T12:30:12Z"}],"graph_snapshots":[{"event_id":"sha256:ca8d77a0171dca66ee3ca86b6b81616b23cde9a416d1e6f53eaf1d13878a158a","target":"graph","created_at":"2026-05-18T01:20:51Z","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":"A set of edges $T$ in a graph $G$ is triangle-independent if $T$ contains at most one edge from each triangle in $G$. Let $\\alpha_1(G)$ denote the maximum size of the triangle-independent set in $G$, and let $\\tau_B(G)$ denote minimum size of a set $F \\subseteq E(G)$ such that $G \\setminus F$ is bipartite. We prove that $$\\alpha_1(G) + \\tau_B(G) \\leq \\frac{|V(G)|^2}{4},$$ verifying a conjecture due to Lehel, and independently Puleo, and a slightly weaker conjecture of Erd\\H{o}s, Gallai and Tuza. Further, we characterize the graphs which attain the equality.","authors_text":"Sergey Norin, Yue Ru Sun","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-02-13T19:54:20Z","title":"Triangle-independent sets vs. cuts"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.04370","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":"sha256:18ffdb8c8baffab7a5785c65b1fff0b64014ffa4c9ff80dbddf8df6f59c51fb7","target":"record","created_at":"2026-05-18T01:20:51Z","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":"735462355a3df50ac1b6fb6d904392561a011a90190e11b110fc26a3cc2a3bc2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-02-13T19:54:20Z","title_canon_sha256":"67e236eea1fb5e3ecbda783a37b57ca0a3cef3f7435a04c0501a5d8e56442a74"},"schema_version":"1.0","source":{"id":"1602.04370","kind":"arxiv","version":1}},"canonical_sha256":"20c313843560f80aa439576e95f8f23628223ece2b284c949f8e4e94d5e3ba70","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"20c313843560f80aa439576e95f8f23628223ece2b284c949f8e4e94d5e3ba70","first_computed_at":"2026-05-18T01:20:51.090058Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:20:51.090058Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"U3erA7fV3PMFXGifu01RLJGvG12O4rTQ98bKSfVMhTGETQmdLbsoOCcNgHgtMfcqp7qb5cptlxp8a7eGqsqIBA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:20:51.090486Z","signed_message":"canonical_sha256_bytes"},"source_id":"1602.04370","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:18ffdb8c8baffab7a5785c65b1fff0b64014ffa4c9ff80dbddf8df6f59c51fb7","sha256:ca8d77a0171dca66ee3ca86b6b81616b23cde9a416d1e6f53eaf1d13878a158a"],"state_sha256":"4e26f8cc40d783afe58cc62c0c0bb90f2559198488f303bb87bf7ae27e695307"}