Definition. EXP (complexity class) [EXP] EXP=⋃k>0TIME(2nk)\text{EXP} = \bigcup_{k > 0}\text{TIME}\left( 2^{n^{k}} \right) The four color map works for all maps, so 4COLORMAP={⟨G⟩:Gis a valid map}\text{4COLORMAP} = \left\{ {\left\langle G \right\rangle:G\ \text{is a valid map}} \right\}.