{"paper":{"title":"On problems about judicious bipartitions of graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Jie Ma, Juan Yan, Xingxing Yu, Yuliang Ji","submitted_at":"2017-01-25T05:03:42Z","abstract_excerpt":"Bollob\\'{a}s and Scott [5] conjectured that every graph $G$ has a balanced bipartite spanning subgraph $H$ such that for each $v\\in V(G)$, $d_H(v)\\ge (d_G(v)-1)/2$. In this paper, we show that every graphic sequence has a realization for which this Bollob\\'{a}s-Scott conjecture holds, confirming a conjecture of Hartke and Seacrest [10]. On the other hand, we give an infinite family of counterexamples to this Bollob\\'{a}s-Scott conjecture, which indicates that $\\lfloor (d_G(v)-1)/2\\rfloor$ (rather than $(d_G(v)-1)/2$) is probably the correct lower bound. We also study bipartitions $V_1, V_2$ of"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.07162","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"}