{"paper":{"title":"Rainbow panconnectivity in a graph collection","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Lihua You, Menghan Ma, Xiaoxue Zhang","submitted_at":"2026-05-25T14:42:49Z","abstract_excerpt":"Let $\\mathbf{G}=\\{G_1,\\dots,G_{n-1}\\}$ be a collection of not necessarily distinct $n$-vertex graphs with the same vertex set $V$. A path $P$ with $V(P)\\subseteq V$ and $|E(P)|\\leq n-1$ is rainbow in $\\mathbf{G}$, if there exists an injection $\\phi\\colon E(P)\\to [n-1]$ such that $e\\in E(G_{\\phi(e)})$ for each $e\\in E(P)$. The graph collection $\\mathbf{G}$ is said to be \\emph{rainbow panconnected} if for every pair of vertices $x,y\\in V$, there exists a rainbow path of $k$ vertices joining $x$ and $y$ in $\\mathbf{G}$ for every integer $k\\in \\left[d_{\\mathbf{G}}(x,y)+1, n\\right]$, where $d_{\\mat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.25907","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.25907/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}