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We introduce stability of a graph in respect of chromatic completion. We prove that the set of chromatic completion edges denoted by $E_\\chi(G),$ which corresponds to $\\zeta(G)$ is unique if and only if $G$ is stable in respect of chromatic completion. Thereafter, chromatic completion and stability is dis"},"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":"1810.13328","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GM","submitted_at":"2018-10-29T06:48:54Z","cross_cats_sorted":[],"title_canon_sha256":"54d70cbfb61df5ee3dde798ab88c2764020a59df2efde2c95ad40c8e30187d31","abstract_canon_sha256":"1c8c1c37f83fedd71898c77e13b41674a3bb264b304d8548682405f9867a524d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:01:49.677275Z","signature_b64":"Za4uGo0lBgFaaLGBvMuAJnwV/g6p/40P/7K8av1CTWfoPPGdh+qJqHjza2mkPLDRfR2ZmuO2G/OVZPD0FLM6DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1dc0c7a7cdce0cd3640f4e1517920beae0901734dcbe912fc49ad1bcc2da4d60","last_reissued_at":"2026-05-18T00:01:49.676789Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:01:49.676789Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Stability in Respect of Chromatic Completion of Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GM","authors_text":"Eunice Mphako-Banda, Johan Kok","submitted_at":"2018-10-29T06:48:54Z","abstract_excerpt":"In an improper colouring an edge $uv$ for which, $c(u)=c(v)$ is called a \\emph{bad edge}. 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