{"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}. The notion of the \\emph{chromatic completion number} of a graph $G$ denoted by $\\zeta(G),$ is the maximum number of edges over all chromatic colourings that can be added to $G$ without adding a bad edge. 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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.13328","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}