{"paper":{"title":"Rectangle Free Coloring of Grids","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Charles Glover, Semmy Purewal, Stephen Fenner, William Gasarch","submitted_at":"2010-05-20T16:12:40Z","abstract_excerpt":"A two-dimensional \\emph{grid} is a set $\\Gnm = [n]\\times[m]$. A grid $\\Gnm$ is \\emph{$c$-colorable} if there is a function $\\chi_{n,m}: \\Gnm \\to [c]$ such that there are no rectangles with all four corners the same color. We address the following question: for which values of $n$ and $m$ is $\\Gnm$ $c$-colorable? This problem can be viewed as a bipartite Ramsey problem and is related to a the Gallai-Witt theorem (also called the multidimensioanl Van Der Waerden's Theorem). We determine (1) \\emph{exactly} which grids are 2-colorable, (2) \\emph{exactly} which grids are 3-colorable, and (3) \\emph{"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1005.3750","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"}