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The local clique cover number of $G$, denoted by $lcc(G)$, is defined as the smallest integer $k$, for which there exists a clique covering for $E(G)$ such that $val_{\\cal C}(v)$ is at most $k$, for every vertex $v\\in V(G)$. In this paper, among other results, we prove that if $G$ is a claw-free graph, then $lcc(G)+\\chi(G)\\leq n+1$."},"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":"1608.07686","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-08-27T10:08:18Z","cross_cats_sorted":[],"title_canon_sha256":"54c1370413f940672fe87311a64331271466e6d664cedecf2e7e0bdba58f83de","abstract_canon_sha256":"01ec1a1d5bacc36a766a004ba34dbd0417627424ef07bf41446ea11fe17f9ec1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:07:50.109140Z","signature_b64":"R7hIkHY1iwsSFSaakdNzXAPhcT1bH01QILdosIbHgxDVZOGOA7/jvxRJANuooNhsCdPmiGUvV6MkjqaraZRvAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"026ae0ad2641e7f1138b5a56b6a8e5f63984a56881d611c35626160b86cbf356","last_reissued_at":"2026-05-18T01:07:50.108659Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:07:50.108659Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Clique Coverings and Claw-free Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Akbar Davoodi, Csilla Bujt\\'as, Ervin Gy\\H{o}ri, Zsolt Tuza","submitted_at":"2016-08-27T10:08:18Z","abstract_excerpt":"Let $\\cal C$ be a clique covering for $E(G)$ and let $v$ be a vertex of $G$. 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