{"paper":{"title":"Graphs with $4$-rainbow index $3$ and $n-1$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Ingo Schiermeyer, Kang Yang, Xueliang Li, Yan Zhao","submitted_at":"2013-12-11T08:19:39Z","abstract_excerpt":"Let $G$ be a nontrivial connected graph with an edge-coloring $c:E(G)\\rightarrow \\{1,2,\\ldots,q\\},$ $q\\in \\mathbb{N}$, where adjacent edges may be colored the same. A tree $T$ in $G$ is called a $rainbow~tree$ if no two edges of $T$ receive the same color. For a vertex set $S\\subseteq V(G)$, a tree that connects $S$ in $G$ is called an {\\it $S$-tree}. The minimum number of colors that are needed in an edge-coloring of $G$ such that there is a rainbow $S$-tree for every $k$-set $S$ of $V(G)$ is called the {\\it $k$-rainbow index} of $G$, denoted by $rx_k(G)$. Notice that an lower bound and an up"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.3069","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"}