{"paper":{"title":"Equivalence between Extendibility and Factor-Criticality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Dingjun Lou, Tao Wang, Zan-Bo Zhang","submitted_at":"2010-11-15T13:47:01Z","abstract_excerpt":"In this paper, we show that if $k\\geq (\\nu+2)/4$, where $\\nu$ denotes the order of a graph, a non-bipartite graph $G$ is $k$-extendable if and only if it is $2k$-factor-critical. If $k\\geq (\\nu-3)/4$, a graph $G$ is $k\\ 1/2$-extendable if and only if it is $(2k+1)$-factor-critical. We also give examples to show that the two bounds are best possible. Our results are answers to a problem posted by Favaron [3] and Yu [11]."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.3381","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"}