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In this note we prove that $\\chi_{s}^{\\prime}(G)\\leq (4k-1)\\Delta (G)-k(2k+1)+1$ for every $k$-degenerate graph $G$. This confirms the strong version of conjecture stated recently by Chang and Narayanan [3]. Our approach allows also to improve the upper bound from [3] for chordless graphs. We get that $% \\chi_{s}^{\\prime}(G)\\leq 4\\Delta -3$ for any chordless graph"},"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":"1301.1992","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-01-09T21:50:54Z","cross_cats_sorted":[],"title_canon_sha256":"34a499afb1fcbee0f58def338b3c2856a1582b047b75b0a68e161d89561161ad","abstract_canon_sha256":"fe10caaf46fd369348aec161f4f558b58ae2dbf6ff8a2e1816c426c100b061a7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:09:33.254522Z","signature_b64":"kcE7KPN4GlZHuc6UIea9PHTGWnAtuOXJAlhCgybhO+xUpl6IBXjylxue/euHsMWQ8BT0ssw7+axa7HjvWggTAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ac6efafdf64e505d5f296faa0d175febd11a86d6b6ff8d4204ca7dd156c33b6f","last_reissued_at":"2026-05-18T01:09:33.254075Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:09:33.254075Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Strong chromatic index of sparse graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Jaros{\\l}aw Grytczuk, Ma{\\l}gorzata \\'Sleszy\\'nska-Nowak, Micha{\\l} D\\k{e}bski","submitted_at":"2013-01-09T21:50:54Z","abstract_excerpt":"A coloring of the edges of a graph $G$ is strong if each color class is an induced matching of $G$. 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