{"paper":{"title":"Good edge-labelings and graphs with girth at least five","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Babak Farzad, Dirk Oliver Theis, Michel Bode","submitted_at":"2011-09-06T09:34:06Z","abstract_excerpt":"A good edge-labeling of a graph [Ara\\'ujo, Cohen, Giroire, Havet, Discrete Appl. Math., forthcoming] is an assignment of numbers to the edges such that for no pair of vertices, there exist two non-decreasing paths.\n  In this paper, we study edge-labeling on graphs with girth at least 5. In particular we verify, under this additional hypothesis, a conjecture by Ara\\'ujo et al. This conjecture states that if the average degree of G is less than 3 and G is minimal without an edge-labeling, then G \\in {C_3,K_{2,3}}. (For the case when the girth is 4, we give a counterexample.)"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.1125","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"}