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In this paper, we introduce the Sylvester coloring conjecture. Moreover, we show that if $G$ is a connected bridgeless cubic graph with $G\\prec P$, then $G=P$. Finally, if $G$ is a connected cubic graph with $G\\prec S$, then $G=S$."},"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":"1201.4472","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2012-01-21T13:48:07Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"58937e21da1d95549fc8e77731a59543a3dca18f722959e3c40ea73f3a219afb","abstract_canon_sha256":"c25645928a6230e6f3d2c7a488bd6ab754f205d672865a3c746a4017d9a8468f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:25:16.352470Z","signature_b64":"283vqS9TXq3gFt5kT9CspAoEhYldyXHMoHWQgSZqCl7DQdekXFu/uPcNTsoa22Dl6+f/cJgExAJHbw4PtANUBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bbc0d6f5a03f322bab4738277ab1a78a74ecc0cea7f490954bee70eb1ed47aed","last_reissued_at":"2026-05-18T03:25:16.351898Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:25:16.351898Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A remark on Petersen coloring conjecture of Jaeger","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.DM","authors_text":"Vahan V. Mkrtchyan","submitted_at":"2012-01-21T13:48:07Z","abstract_excerpt":"If $G$ and $H$ are two cubic graphs, then we write $H\\prec G$, if $G$ admits a proper edge-coloring $f$ with edges of $H$, such that for each vertex $x$ of $G$, there is a vertex $y$ of $H$ with $f(\\partial_G(x))=\\partial_H(y)$. Let $P$ and $S$ be the Petersen graph and the Sylvester graph, respectively. In this paper, we introduce the Sylvester coloring conjecture. Moreover, we show that if $G$ is a connected bridgeless cubic graph with $G\\prec P$, then $G=P$. 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