Abstract A c-coloring of the grid GN,M = N × M is a mapping of GN,M into c such that no four corners forming a rectangle have the same color. In 2009 a challenge was proposed to find a 4-coloring of G17,17. Though a coloring was produced, finding it proved to be difficult. This raises the question of whether there is some complexity lower bound. Consider the following problem: given a partial c-coloring of the GN,M grid, can it be extended to a full c-coloring? We show that this problem is NP-complete. We also give a Fixed Parameter Tractable algorithm for this problem with parameter c.
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