{"paper":{"title":"A note on chromatic blending of colour clusters","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GM","authors_text":"Johan Kok, Muhammad Kamran Jamil, Naduvath Sudev","submitted_at":"2017-02-01T01:57:25Z","abstract_excerpt":"For a colour cluster $\\C =(\\mathcal{C}_1,\\mathcal{C}_2, \\mathcal{C}_3,\\dots,\\mathcal{C}_\\ell)$, $\\mathcal{C}_i$ is a colour class, and $|\\mathcal{C}_i|=r_i \\geq 1$, we investigate a simple connected graph structure $G^{\\C}$, which represents a graphical embodiment of the colour cluster such that the chromatic number $\\chi(G^{\\C})= \\ell,$ and the number of edges is a maximum, denoted $\\varepsilon^+(G^{\\C})$. We also extend the study by inducing new colour clusters recursively by blending the colours of all pairs of adjacent vertices. Recursion repeats until a maximal homogeneous blend between a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.00103","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"}