{"paper":{"title":"List Colouring Squares of Planar Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Bruce Reed, Colin McDiarmid, Fr\\'ed\\'eric Havet, Jan van den Heuvel","submitted_at":"2008-07-21T10:39:56Z","abstract_excerpt":"In 1977, Wegner conjectured that the chromatic number of the square of every planar graph $G$ with maximum degree $\\Delta\\ge8$ is at most $\\bigl\\lfloor\\frac32\\Delta\\bigr\\rfloor+1$. We show that it is at most $\\frac32 \\Delta (1+o(1))$ (where the $o(1)$ is as $\\Delta\\to+\\infty$), and indeed that this is true for the list chromatic number and for more general classes of graphs."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0807.3233","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"}