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These decrease the gaps between the best known upper and lower bounds from $0.0178$ to $0.01$, from $0.0242$ to $0.0123$ and from $0.0724$ to $0.0616$, respectively. We are using local algorithms, therefore, the method also provides upper bounds for the fractional coloring numbers of $1 / 0.44533 \\approx 2.24554$ and"},"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":"1602.02747","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-02-08T00:40:42Z","cross_cats_sorted":["cs.DM","cs.DS"],"title_canon_sha256":"da1ba99a7925109d4cd00dd7660e9a959cfe7e46192de1449baf893603e4c9d7","abstract_canon_sha256":"4979d0b08aa4f4e2bcbb2444f5cc14da19510676e40b824a6781836c30324153"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:21:08.206479Z","signature_b64":"s6nTnl/M0IJjZrjTZ/eIsrjcpAJv1JriF1iKCoBHXYJjexf1AJlWuA7GdWYbXFYw7/6k/SrhWJryHidiawKyBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e64f4510934dd6011a52af7bf5c43c5a74feef6fac1922e05c1aff1a12434437","last_reissued_at":"2026-05-18T01:21:08.205760Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:21:08.205760Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Independent sets and cuts in large-girth regular graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","cs.DS"],"primary_cat":"math.CO","authors_text":"Endre Cs\\'oka","submitted_at":"2016-02-08T00:40:42Z","abstract_excerpt":"We present a local algorithm producing an independent set of expected size $0.44533n$ on large-girth 3-regular graphs and $0.40407n$ on large-girth 4-regular graphs. 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