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Herein, we construct a Steiner triple system of order $v$ with chromatic index at least $(v+3)/2$ for each integer $v \\equiv 3 \\pmod{6}$ such that $v \\geq 15$, with four possible exceptions. We further show that the maximum number of disjoint parallel classes in the systems constructed is sublinear in $v$. Finally, we establish for each order $v \\equiv 15 \\pmod{18}$ that there are at least $v^{v^2(1/6+o(1))}$ n"},"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":"1702.00521","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-02-02T01:47:57Z","cross_cats_sorted":[],"title_canon_sha256":"1f869c74222ec2741ccd9e341caf6b0fc80d3c05339a022a534e1e3b58e1b629","abstract_canon_sha256":"63e1d626cd580b1e1012a011b3dd711e6b37d7cb502a7dad579268ab02e8137b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:26:30.454302Z","signature_b64":"GinPzoWbYyOgbq/MBikc/XFi6vy0KEFEuwX+Gu/L3ZrVEKqiosgQc4mtaZzxfJqK1j3e5fSXnqxIH2+R704mAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c2463ce25905603a792374506d9d197465aa4b4d2213c4f0d62b3331919ea8e4","last_reissued_at":"2026-05-18T00:26:30.453608Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:26:30.453608Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Steiner triple systems with high chromatic index","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Charles Colbourn, Daniel Horsley, Darryn Bryant, Ian M. Wanless","submitted_at":"2017-02-02T01:47:57Z","abstract_excerpt":"It is conjectured that every Steiner triple system of order $v \\neq 7$ has chromatic index at most $(v+3)/2$ when $v \\equiv 3 \\pmod{6}$ and at most $(v+5)/2$ when $v \\equiv 1 \\pmod{6}$. Herein, we construct a Steiner triple system of order $v$ with chromatic index at least $(v+3)/2$ for each integer $v \\equiv 3 \\pmod{6}$ such that $v \\geq 15$, with four possible exceptions. We further show that the maximum number of disjoint parallel classes in the systems constructed is sublinear in $v$. 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