{"paper":{"title":"Paired many-to-many 2-disjoint path cover of balanced hypercubes with faulty edges","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Huazhong L\\\"u","submitted_at":"2018-04-05T16:51:08Z","abstract_excerpt":"As a variant of the well-known hypercube, the balanced hypercube $BH_n$ was proposed as a novel interconnection network topology for parallel computing. It is known that $BH_n$ is bipartite. Assume that $S=\\{s_1,s_2\\}$ and $T=\\{t_1,t_2\\}$ are any two sets of two vertices in different partite sets of $BH_n$ ($n\\geq1$). It has been proved that there exist two vertex-disjoint $s_1,t_1$-path and $s_2,t_2$-path of $BH_n$ covering all vertices of it. In this paper, we prove that there always exist two vertex-disjoint $s_1,t_1$-path and $s_2,t_2$-path covering all vertices of $BH_n$ with at most $2n-"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.01949","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"}