{"paper":{"title":"The minimum size of graphs with given rainbow index","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Thomas Y.H. Liu","submitted_at":"2015-09-24T07:01:52Z","abstract_excerpt":"The concept of $k$-rainbow index $rx_k(G)$ of a connected graph $G$, introduced by Chartrand, Okamoto and Zhang, is a natural generalization of the rainbow connection number. Let $t(n,k,\\ell)$ denote the minimum size of a connected graph $G$ of order $n$ with $rx_k(G)\\leq \\ell$, where $2\\leq \\ell\\leq n-1$ and $2\\leq k\\leq n$. In this paper, we obtain some exact values and some upper bounds for $t(n,k,\\ell)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.07256","kind":"arxiv","version":2},"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"}