{"paper":{"title":"Coloring graphs of various maximum degree from random lists","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Carl Johan Casselgren","submitted_at":"2017-01-03T09:40:13Z","abstract_excerpt":"Let $G=G(n)$ be a graph on $n$ vertices with maximum degree $\\Delta=\\Delta(n)$. Assign to each vertex $v$ of $G$ a list $L(v)$ of colors by choosing each list independently and uniformly at random from all $k$-subsets of a color set $\\mathcal{C}$ of size $\\sigma= \\sigma(n)$. Such a list assignment is called a \\emph{random $(k,\\mathcal{C})$-list assignment}. In this paper, we are interested in determining the asymptotic probability (as $n \\to \\infty$) of the existence of a proper coloring $\\varphi$ of $G$, such that $\\varphi(v) \\in L(v)$ for every vertex $v$ of $G$, a so-called $L$-coloring. We"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.00614","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"}