{"paper":{"title":"Convex Independence in Permutation Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DM","authors_text":"Fu-Hong Liu, Hsiang-Hsuan Liu, Ton Kloks, Wing-Kai Hon","submitted_at":"2016-09-09T04:57:33Z","abstract_excerpt":"A set C of vertices of a graph is P_3-convex if every vertex outside C has at most one neighbor in C. The convex hull \\sigma(A) of a set A is the smallest P_3-convex set that contains A. A set M is convexly independent if for every vertex x \\in M, x \\notin \\sigma(M-x). We show that the maximal number of vertices that a convexly independent set in a permutation graph can have, can be computed in polynomial time."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.02657","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"}