Abstract
In this thesis, we study the 2-distance chromatic number of sparse graphs, namely, planar graphs and graphs with bounded maximum average degree. Upper bounds are obtained by pushing the limits of the discharging method. In particular, we combine it with the potential method. Further, we develop a computer assistance framework for the discharging procedure. We also provide constructions for lower bounds of the 2-distance chromatic number. Finally, we study variants, namely r-hued coloring, injective coloring, and exact square coloring.