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A homogeneous edge-coloring of G is an assignment of an integer m >= 2 and a coloring c:E {\\to} S of the edges of Gsuchthat|S| = mandforanyx{\\in}V,if|E(x)| = mqx+rx with0 <= rx <m, there exists a partition of E(x) in rx color classes of cardinality qx + 1 and other m-rx color classes of cardinality qx. The homogeneous chromatic index \\c{hi}(G) is the least m for which there exists such a coloring. We determine \\c{hi}(G) in the case that G is a complete multigraph, a tree or a comp"},"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":"1203.4531","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-03-20T18:06:40Z","cross_cats_sorted":[],"title_canon_sha256":"4594b57ce6fae37e36aa742da428fd21014380d143c3ad0e64e8337dea28d6ea","abstract_canon_sha256":"f898258ab50e211cc7664965916c96fa01671fd87ca5db4e9ab1759ed8611ba4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:59:38.880517Z","signature_b64":"lcvxpgIwXv7kZvecI0RGE0YO3FVAx0XDAEZXDGOYsFgntpvvHeIhiTPlTdOwcal59omkPmwmWRYfOzdPR3ZkCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a6dc2a9085f2968a4900398ff4c3a548b9e1f7ab95d7084f018d1df1155d737a","last_reissued_at":"2026-05-18T03:59:38.879809Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:59:38.879809Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Homogeneous Edge-Colorings of Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Lucia Marino, Maria Grazia Cinquegrani, Paola Bonacini","submitted_at":"2012-03-20T18:06:40Z","abstract_excerpt":"Let G = (V, E) be a multigraph without loops and for any x {\\in}V let E(x) be the set of edges of G incident to x. 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