{"paper":{"title":"Completely Independent Spanning Trees in $k$-Outerplanar Triangulated Discs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Toru Araki","submitted_at":"2026-06-11T02:47:10Z","abstract_excerpt":"Let $T_{1}, T_{2}, \\dots, T_{k}$ be $k$ spanning trees of a graph $G$. For any pair of vertices $u$ and $v$, if the $u$--$v$ paths in the $k$ spanning trees are pairwise openly disjoint, then the spanning trees are called completely independent spanning trees (CISTs) of $G$. In this paper, we first prove that every 3-connected 2-outerplanar triangulated disc has two completely independent spanning trees. Next, for a 3-connected 3-outerplanar triangulated disc $G$, we provide sufficient conditions for $G$ to have two completely independent spanning trees. We provide an example of a 3-connected "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.12827","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/2606.12827/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"}