{"paper":{"title":"Many-to-many disjoint paths in hypercubes with faulty vertices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Bin Liu, Jun-Ming Xu, Meijie Ma, Xiang-jun Li","submitted_at":"2012-04-19T05:19:57Z","abstract_excerpt":"This paper considers the problem of many-to-many disjoint paths in the hypercube $Q_n$ with $f$ faulty vertices and obtains the following result. For any integer $k$ with $1\\leq k\\leq n-2$, any two sets $S$ and $T$ of $k$ fault-free vertices in different parts of $Q_n\\ (n\\geq 3)$, if $f\\leq 2n-2k-3$ and each fault-free vertex has at least two fault-free neighbors, then there exist $k$ fully disjoint fault-free paths linking $S$ and $T$ which contain at least $2^n-2f$ vertices. This result improves some known results in a sense."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.4252","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"}