{"paper":{"title":"Choosability and paintability of the lexicographic product of graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Bal\\'azs Keszegh, Xuding Zhu","submitted_at":"2015-02-13T13:13:11Z","abstract_excerpt":"This paper studies the choice number and paint number of the lexicographic product of graphs. We prove that if $G$ has maximum degree $\\Delta$, then for any graph $H$ on $n$ vertices $ch(G[H]) \\le (4\\Delta+2)(ch(H) +\\log_2 n)$ and $\\chi_P(G[H]) \\le (4\\Delta+2) (\\chi_P(H)+ \\log_2 n)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.03977","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"}