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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."},"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":"1602.04370","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-02-13T19:54:20Z","cross_cats_sorted":[],"title_canon_sha256":"67e236eea1fb5e3ecbda783a37b57ca0a3cef3f7435a04c0501a5d8e56442a74","abstract_canon_sha256":"735462355a3df50ac1b6fb6d904392561a011a90190e11b110fc26a3cc2a3bc2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:20:51.090486Z","signature_b64":"U3erA7fV3PMFXGifu01RLJGvG12O4rTQ98bKSfVMhTGETQmdLbsoOCcNgHgtMfcqp7qb5cptlxp8a7eGqsqIBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"20c313843560f80aa439576e95f8f23628223ece2b284c949f8e4e94d5e3ba70","last_reissued_at":"2026-05-18T01:20:51.090058Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:20:51.090058Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Triangle-independent sets vs. cuts","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Sergey Norin, Yue Ru Sun","submitted_at":"2016-02-13T19:54:20Z","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 $G$. 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