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For every graph $G$ and every $c\\in\\mathbb{Z}_{+}^{V(G)}$, the weighted chromatic number of $(G,c)$ is the minimum cardinality of a multi-set $\\mathcal{F}$ of stable sets of $G$ such that every $v\\in V(G)$ belongs to at least $c_v$ members of $\\mathcal{F}$.\n  We prove that every h-perfect line-graph and every t-perfect claw-free graph $G$ has the integer round-up property for the chromatic number: for every no"},"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":"1406.0757","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-06-03T15:42:11Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"08514a20b4591e55f66746e735f12661eec10f2bddadd1de52e0e4f5ce2f7722","abstract_canon_sha256":"ca078b68265c0a77f4fa0d2ea0b21ac6baf04632f3114fba170c85b386642ea8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:50:32.897588Z","signature_b64":"nVRckeLy3pwddE2wieK8mpUwy8xHYymijQYEaEAL4Zh6mTiKfN2WrfdwjjxCjnaY5TEuLTQ2Irj2i6avWMbAAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"97d9372bb81879d2188d32f22343f0bd7f0a24eceb857ff252e38e2a9e7cb368","last_reissued_at":"2026-05-18T02:50:32.897102Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:50:32.897102Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Integer round-up property for the chromatic number of some h-perfect graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"math.CO","authors_text":"Yohann Benchetrit","submitted_at":"2014-06-03T15:42:11Z","abstract_excerpt":"A graph is h-perfect if its stable set polytope can be completely described by non-negativity, clique and odd-hole constraints. 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