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A result of Rhys Price Jones from 1975 says that every connected hypergraph $G$ satisfies $\\chi(G) \\leq \\Delta(G) + 1$ and equality holds if and only if $G$ is a complete graph, an odd cycle, or $G$ has just one (hyper-)edge. By a result of Bjarne Toft from 1970 it follows that every hypergraph $G$ satisfies $\\chi(G) \\leq \\lambda(G) + 1$. In this paper, we show that a hypergraph $G$ with $\\lambda(G) \\geq 3$ satisfies $\\c"},"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":"1806.08567","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-06-22T09:20:39Z","cross_cats_sorted":[],"title_canon_sha256":"29304505ddf8d1f46a5cbc852a5fa84caac9a2f34091e0de08ffbe1421383bc5","abstract_canon_sha256":"69053025d30de72dc5cbeb181f33aa2666e50613d35d500e43d60047430b215e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:11:56.567253Z","signature_b64":"mtiEr0otvuWF4P1TB30v2Pdt/z8ZP3PeuHGp8XbQZyMglzVvPdANGWm1j4GtNbZt9yi+6iQmvlhR3CRpA45JAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4af90186cdf269429b72d28b0d170e033e0f3a4d6624fac7ae75244efc4018e1","last_reissued_at":"2026-05-18T00:11:56.566591Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:11:56.566591Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Coloring hypergraphs of low connectivity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Bjarne Toft, Michael Stiebitz, Thomas Schweser","submitted_at":"2018-06-22T09:20:39Z","abstract_excerpt":"For a hypergraph $G$, let $\\chi(G), \\Delta(G),$ and $\\lambda(G)$ denote the chromatic number, the maximum degree, and the maximum local edge connectivity of $G$, respectively. A result of Rhys Price Jones from 1975 says that every connected hypergraph $G$ satisfies $\\chi(G) \\leq \\Delta(G) + 1$ and equality holds if and only if $G$ is a complete graph, an odd cycle, or $G$ has just one (hyper-)edge. By a result of Bjarne Toft from 1970 it follows that every hypergraph $G$ satisfies $\\chi(G) \\leq \\lambda(G) + 1$. 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