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The first result gives an affirmative answer to a question posed by Tuza in 1992, and the second implies the following strong form of a conjecture of Diwan, Kenkre and Vishwanathan: If an undirected"},"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":"1403.8127","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-03-31T18:55:52Z","cross_cats_sorted":[],"title_canon_sha256":"e9997993285c16a6143e270cceeab5bc098e61f0ce16a9ccb7dc65a2aa4b14d4","abstract_canon_sha256":"629a2ce0c1e9b6381fef30675d552ea13a965990ca2de0b38442fd068f0562b8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:55:11.779375Z","signature_b64":"TzGLW2vyX8VxDis/dh8mififj5eOT/T/0nhWpjz1Vy/9tc2IyeaK537ksEtb9z8rW6BAFKrJpmIyQLOybQ12Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"aa44b4d8d623152570fa07683a2640ca87d00bad4078b770ba145f51be12df3b","last_reissued_at":"2026-05-18T02:55:11.778934Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:55:11.778934Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Coloring Digraphs with Forbidden Cycles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Jie Ma, Wenan Zang, Zhibin Chen","submitted_at":"2014-03-31T18:55:52Z","abstract_excerpt":"Let $k$ and $r$ be two integers with $k \\ge 2$ and $k\\ge r \\ge 1$. 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