{"paper":{"title":"Improved lower bounds on the number of edges in list critical and online list critical graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Hal Kierstead, Landon Rabern","submitted_at":"2014-06-28T04:44:58Z","abstract_excerpt":"We prove that every $k$-list-critical graph ($k \\ge 7$) on $n \\ge k+2$ vertices has at least $\\frac12 \\left(k-1 + \\frac{k-3}{(k-c)(k-1) + k-3}\\right)n$ edges where $c = (k-3)\\left(\\frac12 - \\frac{1}{(k-1)(k-2)}\\right)$. This improves the bound established by Kostochka and Stiebitz. The same bound holds for online $k$-list-critical graphs, improving the bound established by Riasat and Schauz. Both bounds follow from a more general result stating that either a graph has many edges or it has an Alon-Tarsi orientable induced subgraph satisfying a certain degree condition."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.7355","kind":"arxiv","version":2},"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"}