{"paper":{"title":"Finding all Convex Cuts of a Plane Graph in Polynomial Time","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"cs.DS","authors_text":"Henning Meyerhenke, Roland Glantz","submitted_at":"2013-03-18T18:21:45Z","abstract_excerpt":"Convexity is a notion that has been defined for subsets of $\\RR^n$ and for subsets of general graphs. A convex cut of a graph $G=(V, E)$ is a $2$-partition $V_1 \\dot{\\cup} V_2=V$ such that both $V_1$ and $V_2$ are convex, \\ie shortest paths between vertices in $V_i$ never leave $V_i$, $i \\in \\{1, 2\\}$. Finding convex cuts is $\\mathcal{NP}$-hard for general graphs. To characterize convex cuts, we employ the Djokovic relation, a reflexive and symmetric relation on the edges of a graph that is based on shortest paths between the edges' end vertices.\n  It is known for a long time that, if $G$ is b"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.4349","kind":"arxiv","version":3},"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"}