{"paper":{"title":"The 3-rainbow index and connected dominating sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Qingqiong Cai, Xueliang Li, Yan Zhao","submitted_at":"2014-04-09T06:34:25Z","abstract_excerpt":"A tree in an edge-colored graph is said to be rainbow if no two edges on the tree share the same color. An edge-coloring of $G$ is called 3-rainbow if for any three vertices in $G$, there exists a rainbow tree connecting them. The 3-rainbow index $rx_3(G)$ of $G$ is defined as the minimum number of colors that are needed in a 3-rainbow coloring of $G$. This concept, introduced by Chartrand et al., can be viewed as a generalization of the rainbow connection. In this paper, we study the 3-rainbow index by using connected three-way dominating sets and 3-dominating sets. We shown that for every co"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.2377","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"}