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- W1614138082 abstract "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{exactly} which grids are 4-colorable. We use combinatorics, finite fields, and tournament graphs." @default.
- W1614138082 created "2016-06-24" @default.
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- W1614138082 date "2018-12-27" @default.
- W1614138082 modified "2023-09-27" @default.
- W1614138082 title "Rectangle-Free Coloring of Grids" @default.
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- W1614138082 doi "https://doi.org/10.1142/9789813279735_0023" @default.
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