The Complexity of Grid Coloring

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