{"paper":{"title":"Minimum diameter and cycle-diameter orientations on planar graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC"],"primary_cat":"cs.DM","authors_text":"Nili Guttmann-Beck, Refael Hassin","submitted_at":"2011-05-24T14:04:00Z","abstract_excerpt":"Let G be an edge weighted undirected graph. For every pair of nodes consider the shortest cycle containing these nodes in G. The cycle diameter of G is the maximum length of a cycle in this set. Let H be a directed graph obtained by directing the edges of G. The cycle diameter of H is similarly defined except for that cycles are replaced by directed closed walks. Is there always an orientation H of G whose cycle diameter is bounded by a constant times the cycle diameter of G? We prove this property for planar graphs. These results have implications on the problem of approximating an orientatio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.4770","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"}