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Not all graphs have such a decomposition, but Baudon, Bensmail, Przyby{\\l}o, and Wo\\'zniak conjectured that if $G$ can be decomposed into locally irregular subgraphs, then $\\chi_{\\rm irr}'(G)\\leq 3$. In support of this conjecture, Przyby{\\l}o showed that $\\chi_{\\rm irr}'(G)\\leq 3$ holds whenever $G$ has minimum degree at least $10^{10}$.\n  Here we prove that every bipa"},"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":"1604.00235","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-04-01T13:30:13Z","cross_cats_sorted":[],"title_canon_sha256":"7755d3b81022b4aeb95052cfc48c132e9852bd1381124b7d6978e836baf75915","abstract_canon_sha256":"5e4bb726c60099ee40dbd5f172376ee55ae6988f6b871b32e29e7ba1cabddad6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:17:54.240623Z","signature_b64":"ifV0PyXyngfy8dEv3kB5s4Ii+I8kWDeDEfvT/lAuo1F9kcdEBgJt2XhtmkAv5pX8WnRa4aCeTba9soG0ZGKKDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ab5baf049398766687ab98dce423544d86a655ef952037a049fa645c049f7c3c","last_reissued_at":"2026-05-18T01:17:54.239935Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:17:54.239935Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Decomposing graphs into a constant number of locally irregular subgraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Carsten Thomassen, Julien Bensmail, Martin Merker","submitted_at":"2016-04-01T13:30:13Z","abstract_excerpt":"A graph is locally irregular if no two adjacent vertices have the same degree. 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