{"paper":{"title":"The generalized $4$-connectivity of bubble-sort graphs","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Bo Zhou, Leyou Xu","submitted_at":"2023-03-24T08:59:44Z","abstract_excerpt":"For $S\\subseteq V(G)$ with $|S|\\ge 2$, let $\\kappa_G (S)$ denote the maximum number of internally disjoint trees connecting $S$ in $G$. For $2\\le k\\le n$, the generalized $k$-connectivity $\\kappa_k(G)$ of an $n$-vertex connected graph $G$ is defined to be $\\kappa_k(G)=\\min \\{\\kappa_G(S): S\\in V(G) \\mbox{ and } |S|=k\\}$. The generalized $k$-connectivity can serve for measuring the fault tolerance of an interconnection network. The bubble-sort graph $B_n$ for $n\\ge 2$ is a Cayley graph over the symmetric group of permutations on $[n]$ generated by transpositions from the set $\\{[1,2],[2,3],\\dots"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2303.13864","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/2303.13864/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"}