{"paper":{"title":"Independence number of edge-chromatic critical graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Guangming Jing, Guantao Chen, Songling Shan, Yan Cao","submitted_at":"2018-05-15T19:00:27Z","abstract_excerpt":"Let $G$ be a simple graph with maximum degree $\\Delta(G)$ and chromatic index $\\chi'(G)$. A classic result of Vizing indicates that either $\\chi'(G )=\\Delta(G)$ or $\\chi'(G )=\\Delta(G)+1$. The graph $G$ is called $\\Delta$-critical if $G$ is connected, $\\chi'(G )=\\Delta(G)+1$ and for any $e\\in E(G)$, $\\chi'(G-e)=\\Delta(G)$. Let $G$ be an $n$-vertex $\\Delta$-critical graph. Vizing conjectured that $\\alpha(G)$, the independence number of $G$, is at most $\\frac{n}{2}$. The current best result on this conjecture, shown by Woodall, is that $\\alpha(G)<\\frac{3n}{5}$. We show that for any given $\\varep"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.05996","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"}