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We prove the conjecture for Generalized Petersen graphs.\n  We indicate that a coloring with the same properties might exist for any subcubic graph. We confirm this statement for all subcubic trees."},"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":"1901.11339","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-01-31T13:09:24Z","cross_cats_sorted":[],"title_canon_sha256":"4e9661b69c42d124d196b77ebf03d0b8da0e7fe00552d9a31df136b76fc74da2","abstract_canon_sha256":"db62ed27d840e6a0232b3102d0de3c84ae45ad9f78d5a6ab1b1314b4255b3373"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:55:02.141994Z","signature_b64":"nD9iJudInxEQexJWWQzXtvEyxsn6KecMkHS1VW+2TbjdMPDikStwSLumk02gngPOlzvohUBJfyBoaMF+N605Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5a1cd95f4af9fe14ead9d4e89b695cbf11c35931ee59af8719a6fa1f942ea8c2","last_reissued_at":"2026-05-17T23:55:02.141380Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:55:02.141380Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Decomposition of cubic graphs related to Wegner's conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"J\\'anos Bar\\'at","submitted_at":"2019-01-31T13:09:24Z","abstract_excerpt":"Thomassen formulated the following conjecture: Every $3$-connected cubic graph has a red-blue vertex coloring such that the blue subgraph has maximum degree $1$ (that is, it consists of a matching and some isolated vertices) and the red subgraph has minimum degree at least $1$ and contains no $3$-edge path. 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