{"paper":{"title":"Structure connectivity and substructure connectivity of twisted hypercubes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Dong Li, Huiqing Liu, Xiaolan Hu","submitted_at":"2018-03-22T15:31:20Z","abstract_excerpt":"Let $G$ be a graph and $T$ a certain connected subgraph of $G$. The $T$-structure connectivity $\\kappa(G; T)$ (or resp., $T$-substructure connectivity $\\kappa^{s}(G; T)$) of $G$ is the minimum number of a set of subgraphs $\\mathcal{F}=\\{T_{1}, T_{2}, \\ldots, T_{m}\\}$ (or resp., $\\mathcal{F}=\\{T^{'}_{1}, T^{'}_{2}, \\ldots, T^{'}_{m}\\}$) such that $T_{i}$ is isomorphic to $T$ (or resp., $T^{'}_{i}$ is a connected subgraph of $T$) for every $1\\leq i \\leq m$, and $\\mathcal{F}$'s removal will disconnect $G$. The twisted hypercube $H_{n}$ is a new variant of hypercubes with asymptotically optimal di"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.08408","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":""},"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"}