{"paper":{"title":"A note on list-coloring powers of graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Benjamin Reiniger, Elyse Yeager, Nicholas Kosar, Sarka Petrickova","submitted_at":"2013-09-30T02:10:16Z","abstract_excerpt":"Recently, Kim and Park have found an infinite family of graphs whose squares are not chromatic-choosable. Xuding Zhu asked whether there is some $k$ such that all $k$th power graphs are chromatic-choosable. We answer this question in the negative: we show that there is a positive constant $c$ such that for any $k$ there is a family of graphs $G$ with $\\chi(G^k)$ unbounded and $\\chi_{\\ell}(G^k)\\geq c \\chi(G^k) \\log \\chi(G^k)$. We also provide an upper bound, $\\chi_{\\ell}(G^k)<\\chi(G^k)^3$ for $k>1$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.7705","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"}