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In this paper, we show that the following result: if a 3-edge-connected bipartite graph $G$ with minimum degree $\\delta$ contains a vertex $u\\in V(G)$ such that $d_G(u)=\\delta$ and $G-u"},"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":"1307.1863","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-07-07T13:21:54Z","cross_cats_sorted":[],"title_canon_sha256":"7685beaf227efd32e44556e165fb78b0e6bbed97e9963b0a157c45c5c1be6dc7","abstract_canon_sha256":"69f4c0f72cf39c3c51b256646b8d94eb19f8becd70710548f2d8ee883d6aa844"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:19:03.314525Z","signature_b64":"44O+FSLP/ceM5EJaCKGJlnqKrVdR0pXQttjGDZffpPNrdjoXUvaCk9A7FZtLJXdHpvFbhrOTLAg5GTH3wA+eCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"03d61ac63ddc5bbfe21f0bf6caa9259f8227ebcca93e8ee5e24eefe3ba4e0146","last_reissued_at":"2026-05-18T03:19:03.313969Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:19:03.313969Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Vertex-Coloring Edge-Weighting of Bipartite Graphs with Two Edge Weights","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Hongliang Lu","submitted_at":"2013-07-07T13:21:54Z","abstract_excerpt":"Let $G$ be a graph and $\\mathcal {S}$ be a subset of $Z$. 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